Solve the System of Equations 4x-2y+3z=-3 2x-3y+2z=1 6x+10z=-2

$4 x - 2 y + 3 z = - 3$ $2 x - 3 y + 2 z = 1$ $6 x + 10 z = - 2$

Step 1

Solve for $x$ in $4 x - 2 y + 3 z = - 3$ .

Move all terms not containing $x$ to the right side of the equation.

Add $2 y$ to both sides of the equation.

$4 x + 3 z = - 3 + 2 y$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Subtract $3 z$ from both sides of the equation.

$4 x = - 3 + 2 y - 3 z$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$4 x = - 3 + 2 y - 3 z$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Divide each term in $4 x = - 3 + 2 y - 3 z$ by $4$ and simplify.

Divide each term in $4 x = - 3 + 2 y - 3 z$ by $4$ .

$\frac{4 x}{4} = \frac{- 3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Divide $x$ by $1$ .

$x = \frac{- 3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = \frac{- 3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = \frac{- 3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{3}{4} + \frac{2 y}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 y$ .

$x = - \frac{3}{4} + \frac{2 (y)}{4} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = - \frac{3}{4} + \frac{2 y}{2 \cdot 2} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Cancel the common factor.

$x = - \frac{3}{4} + \frac{2 y}{2 \cdot 2} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Rewrite the expression.

$x = - \frac{3}{4} + \frac{y}{2} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} + \frac{- 3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Move the negative in front of the fraction.

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$2 x - 3 y + 2 z = 1$

$6 x + 10 z = - 2$

Step 2

Replace all occurrences of $x$ with $- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$ in each equation.

Replace all occurrences of $x$ in $2 x - 3 y + 2 z = 1$ with $- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$ .

$2 (- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Simplify the left side.

Simplify $2 (- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}) - 3 y + 2 z$ .

Simplify each term.

Apply the distributive property.

$2 (- \frac{3}{4}) + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Simplify.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$2 (\frac{- 3}{4}) + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $2$ out of $4$ .

$2 (\frac{- 3}{2 (2)}) + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Cancel the common factor.

$2 (\frac{- 3}{2 \cdot 2}) + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Rewrite the expression.

$\frac{- 3}{2} + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$\frac{- 3}{2} + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{- 3}{2} + 2 (\frac{y}{2}) + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Rewrite the expression.

$\frac{- 3}{2} + y + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$\frac{- 3}{2} + y + 2 (- \frac{3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 z}{4}$ into the numerator.

$\frac{- 3}{2} + y + 2 (\frac{- 3 z}{4}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $2$ out of $4$ .

$\frac{- 3}{2} + y + 2 (\frac{- 3 z}{2 (2)}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Cancel the common factor.

$\frac{- 3}{2} + y + 2 (\frac{- 3 z}{2 \cdot 2}) - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Rewrite the expression.

$\frac{- 3}{2} + y + \frac{- 3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$\frac{- 3}{2} + y + \frac{- 3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$\frac{- 3}{2} + y + \frac{- 3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{3}{2} + y + \frac{- 3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Move the negative in front of the fraction.

$- \frac{3}{2} + y - \frac{3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$- \frac{3}{2} + y - \frac{3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$- \frac{3}{2} + y - \frac{3 z}{2} - 3 y + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Subtract $3 y$ from $y$ .

$- \frac{3}{2} - 2 y - \frac{3 z}{2} + 2 z = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

To write $2 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3}{2} - 2 y - \frac{3 z}{2} + 2 z \cdot \frac{2}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Combine $2 z$ and $\frac{2}{2}$ .

$- \frac{3}{2} - 2 y - \frac{3 z}{2} + \frac{2 z \cdot 2}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Combine the numerators over the common denominator.

$- \frac{3}{2} - 2 y + \frac{- 3 z + 2 z \cdot 2}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Combine the numerators over the common denominator.

$- 2 y + \frac{- 3 - 3 z + 2 z \cdot 2}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Multiply $2$ by $2$ .

$- 2 y + \frac{- 3 - 3 z + 4 z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Add $- 3 z$ and $4 z$ .

$- 2 y + \frac{- 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 y \cdot \frac{2}{2} + \frac{- 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Combine $- 2 y$ and $\frac{2}{2}$ .

$\frac{- 2 y \cdot 2}{2} + \frac{- 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Combine the numerators over the common denominator.

$\frac{- 2 y \cdot 2 - 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Multiply $2$ by $- 2$ .

$\frac{- 4 y - 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $- 1$ out of $- 4 y$ .

$\frac{- (4 y) - 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (4 y) - 1 \cdot 3 + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $- 1$ out of $- (4 y) - 1 (3)$ .

$\frac{- (4 y + 3) + z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $- 1$ out of $z$ .

$\frac{- (4 y + 3) - 1 (- z)}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Factor $- 1$ out of $- (4 y + 3) - 1 (- z)$ .

$\frac{- (4 y + 3 - z)}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Simplify the expression.

Rewrite $- (4 y + 3 - z)$ as $- 1 (4 y + 3 - z)$ .

$\frac{- 1 (4 y + 3 - z)}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Move the negative in front of the fraction.

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 x + 10 z = - 2$

Replace all occurrences of $x$ in $6 x + 10 z = - 2$ with $- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$ .

$6 (- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the left side.

Simplify $6 (- \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}) + 10 z$ .

Simplify each term.

Apply the distributive property.

$6 (- \frac{3}{4}) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$6 (\frac{- 3}{4}) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $6$ .

$2 (3) (\frac{- 3}{4}) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $4$ .

$2 \cdot (3 (\frac{- 3}{2 \cdot 2})) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor.

$2 \cdot (3 (\frac{- 3}{2 \cdot 2})) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$3 (\frac{- 3}{2}) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$3 (\frac{- 3}{2}) + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $3$ and $\frac{- 3}{2}$ .

$\frac{3 \cdot - 3}{2} + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $3$ by $- 3$ .

$\frac{- 9}{2} + 6 (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{- 9}{2} + 2 (3) (\frac{y}{2}) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor.

$\frac{- 9}{2} + 2 \cdot (3 (\frac{y}{2})) + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$\frac{- 9}{2} + 3 y + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{- 9}{2} + 3 y + 6 (- \frac{3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 z}{4}$ into the numerator.

$\frac{- 9}{2} + 3 y + 6 (\frac{- 3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $6$ .

$\frac{- 9}{2} + 3 y + 2 (3) (\frac{- 3 z}{4}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $4$ .

$\frac{- 9}{2} + 3 y + 2 \cdot (3 (\frac{- 3 z}{2 \cdot 2})) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor.

$\frac{- 9}{2} + 3 y + 2 \cdot (3 (\frac{- 3 z}{2 \cdot 2})) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$\frac{- 9}{2} + 3 y + 3 (\frac{- 3 z}{2}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{- 9}{2} + 3 y + 3 (\frac{- 3 z}{2}) + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $3$ and $\frac{- 3 z}{2}$ .

$\frac{- 9}{2} + 3 y + \frac{3 (- 3 z)}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $- 3$ by $3$ .

$\frac{- 9}{2} + 3 y + \frac{- 9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{- 9}{2} + 3 y + \frac{- 9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{9}{2} + 3 y + \frac{- 9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Move the negative in front of the fraction.

$- \frac{9}{2} + 3 y - \frac{9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{9}{2} + 3 y - \frac{9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{9}{2} + 3 y - \frac{9 z}{2} + 10 z = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

To write $10 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9}{2} + 3 y - \frac{9 z}{2} + 10 z \cdot \frac{2}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $10 z$ and $\frac{2}{2}$ .

$- \frac{9}{2} + 3 y - \frac{9 z}{2} + \frac{10 z \cdot 2}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$- \frac{9}{2} + 3 y + \frac{- 9 z + 10 z \cdot 2}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$3 y + \frac{- 9 - 9 z + 10 z \cdot 2}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $2$ by $10$ .

$3 y + \frac{- 9 - 9 z + 20 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Add $- 9 z$ and $20 z$ .

$3 y + \frac{- 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 y \cdot \frac{2}{2} + \frac{- 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $3 y$ and $\frac{2}{2}$ .

$\frac{3 y \cdot 2}{2} + \frac{- 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$\frac{3 y \cdot 2 - 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $2$ by $3$ .

$\frac{6 y - 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{6 y - 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{6 y - 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{6 y - 9 + 11 z}{2} = - 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Step 3

Solve for $y$ in $\frac{6 y - 9 + 11 z}{2} = - 2$ .

Multiply both sides by $2$ .

$\frac{6 y - 9 + 11 z}{2} \cdot 2 = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify.

Simplify the left side.

Simplify $\frac{6 y - 9 + 11 z}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{6 y - 9 + 11 z}{2} \cdot 2 = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$6 y - 9 + 11 z = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y - 9 + 11 z = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Move $- 9$ .

$6 y + 11 z - 9 = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y + 11 z - 9 = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y + 11 z - 9 = - 2 \cdot 2$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the right side.

Multiply $- 2$ by $2$ .

$6 y + 11 z - 9 = - 4$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y + 11 z - 9 = - 4$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y + 11 z - 9 = - 4$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $11 z$ from both sides of the equation.

$6 y - 9 = - 4 - 11 z$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Add $9$ to both sides of the equation.

$6 y = - 4 - 11 z + 9$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Add $- 4$ and $9$ .

$6 y = - 11 z + 5$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$6 y = - 11 z + 5$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Divide each term in $6 y = - 11 z + 5$ by $6$ and simplify.

Divide each term in $6 y = - 11 z + 5$ by $6$ .

$\frac{6 y}{6} = \frac{- 11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Divide $y$ by $1$ .

$y = \frac{- 11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = \frac{- 11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = \frac{- 11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$- \frac{4 y + 3 - z}{2} = 1$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Step 4

Replace all occurrences of $y$ with $- \frac{11 z}{6} + \frac{5}{6}$ in each equation.

Replace all occurrences of $y$ in $- \frac{4 y + 3 - z}{2} = 1$ with $- \frac{11 z}{6} + \frac{5}{6}$ .

$- \frac{4 (- \frac{11 z}{6} + \frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the left side.

Simplify $- \frac{4 (- \frac{11 z}{6} + \frac{5}{6}) + 3 - z}{2}$ .

Simplify the numerator.

Apply the distributive property.

$- \frac{4 (- \frac{11 z}{6}) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11 z}{6}$ into the numerator.

$- \frac{4 (\frac{- 11 z}{6}) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $4$ .

$- \frac{2 (2) (\frac{- 11 z}{6}) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $6$ .

$- \frac{2 \cdot (2 (\frac{- 11 z}{2 \cdot 3})) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor.

$- \frac{2 \cdot (2 (\frac{- 11 z}{2 \cdot 3})) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$- \frac{2 (\frac{- 11 z}{3}) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{2 (\frac{- 11 z}{3}) + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $2$ and $\frac{- 11 z}{3}$ .

$- \frac{\frac{2 (- 11 z)}{3} + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $- 11$ by $2$ .

$- \frac{\frac{- 22 z}{3} + 4 (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$- \frac{\frac{- 22 z}{3} + 2 (2) (\frac{5}{6}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $2$ out of $6$ .

$- \frac{\frac{- 22 z}{3} + 2 \cdot (2 (\frac{5}{2 \cdot 3})) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Cancel the common factor.

$- \frac{\frac{- 22 z}{3} + 2 \cdot (2 (\frac{5}{2 \cdot 3})) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite the expression.

$- \frac{\frac{- 22 z}{3} + 2 (\frac{5}{3}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{\frac{- 22 z}{3} + 2 (\frac{5}{3}) + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $2$ and $\frac{5}{3}$ .

$- \frac{\frac{- 22 z}{3} + \frac{2 \cdot 5}{3} + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $2$ by $5$ .

$- \frac{\frac{- 22 z}{3} + \frac{10}{3} + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Move the negative in front of the fraction.

$- \frac{- \frac{22 z}{3} + \frac{10}{3} + 3 - z}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

To write $- z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{- \frac{22 z}{3} - z \cdot \frac{3}{3} + \frac{10}{3} + 3}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $- z$ and $\frac{3}{3}$ .

$- \frac{- \frac{22 z}{3} + \frac{- z \cdot 3}{3} + \frac{10}{3} + 3}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$- \frac{\frac{- 22 z - z \cdot 3}{3} + \frac{10}{3} + 3}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$- \frac{\frac{- 22 z - z \cdot 3 + 10}{3} + 3}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{\frac{- 22 z - z \cdot 3 + 10}{3} + 3 \cdot \frac{3}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine $3$ and $\frac{3}{3}$ .

$- \frac{\frac{- 22 z - z \cdot 3 + 10}{3} + \frac{3 \cdot 3}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Combine the numerators over the common denominator.

$- \frac{\frac{- 22 z - z \cdot 3 + 10 + 3 \cdot 3}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Reorder terms.

$- \frac{\frac{- 1 \cdot (3 z) - 22 z + 3 \cdot 3 + 10}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite $\frac{- 1 \cdot 3 z - 22 z + 3 \cdot 3 + 10}{3}$ in a factored form.

Multiply $- 1$ by $3$ .

$- \frac{\frac{- 3 z - 22 z + 3 \cdot 3 + 10}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $3$ by $3$ .

$- \frac{\frac{- 3 z - 22 z + 9 + 10}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Subtract $22 z$ from $- 3 z$ .

$- \frac{\frac{- 25 z + 9 + 10}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Add $9$ and $10$ .

$- \frac{\frac{- 25 z + 19}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{\frac{- 25 z + 19}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{\frac{- 25 z + 19}{3}}{2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{- 25 z + 19}{3} \cdot \frac{1}{2}) = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $\frac{- 25 z + 19}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{- 25 z + 19}{3}$ by $\frac{1}{2}$ .

$- \frac{- 25 z + 19}{3 \cdot 2} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $3$ by $2$ .

$- \frac{- 25 z + 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$- \frac{- 25 z + 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $- 1$ out of $- 25 z$ .

$- \frac{- (25 z) + 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Rewrite $19$ as $- 1 (- 19)$ .

$- \frac{- (25 z) - 1 \cdot - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Factor $- 1$ out of $- (25 z) - 1 (- 19)$ .

$- \frac{- (25 z - 19)}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Simplify the expression.

Rewrite $- (25 z - 19)$ as $- 1 (25 z - 19)$ .

$- \frac{- 1 (25 z - 19)}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Move the negative in front of the fraction.

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $- 1$ by $- 1$ .

$1 (\frac{25 z - 19}{6}) = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Multiply $\frac{25 z - 19}{6}$ by $1$ .

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$

Replace all occurrences of $y$ in $x = - \frac{3}{4} + \frac{y}{2} - \frac{3 z}{4}$ with $- \frac{11 z}{6} + \frac{5}{6}$ .

$x = - \frac{3}{4} + \frac{- \frac{11 z}{6} + \frac{5}{6}}{2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the right side.

Simplify $- \frac{3}{4} + \frac{- \frac{11 z}{6} + \frac{5}{6}}{2} - \frac{3 z}{4}$ .

Find the common denominator.

Multiply $\frac{- \frac{11 z}{6} + \frac{5}{6}}{2}$ by $\frac{2}{2}$ .

$x = - \frac{3}{4} + \frac{- \frac{11 z}{6} + \frac{5}{6}}{2} \cdot \frac{2}{2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Multiply $\frac{- \frac{11 z}{6} + \frac{5}{6}}{2}$ by $\frac{2}{2}$ .

$x = - \frac{3}{4} + \frac{(- \frac{11 z}{6} + \frac{5}{6}) \cdot 2}{2 \cdot 2} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Multiply $2$ by $2$ .

$x = - \frac{3}{4} + \frac{(- \frac{11 z}{6} + \frac{5}{6}) \cdot 2}{4} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{3}{4} + \frac{(- \frac{11 z}{6} + \frac{5}{6}) \cdot 2}{4} - \frac{3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$x = \frac{- 3 + (- \frac{11 z}{6} + \frac{5}{6}) \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify each term.

Apply the distributive property.

$x = \frac{- 3 - \frac{11 z}{6} \cdot 2 + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11 z}{6}$ into the numerator.

$x = \frac{- 3 + \frac{- 11 z}{6} \cdot 2 + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $2$ out of $6$ .

$x = \frac{- 3 + \frac{- 11 z}{2 (3)} \cdot 2 + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor.

$x = \frac{- 3 + \frac{- 11 z}{2 \cdot 3} \cdot 2 + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Rewrite the expression.

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{6} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{2 (3)} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor.

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{2 \cdot 3} \cdot 2 - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Rewrite the expression.

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- 3 + \frac{- 11 z}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Move the negative in front of the fraction.

$x = \frac{- 3 - \frac{11 z}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- 3 - \frac{11 z}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{- \frac{11 z}{3} - 3 \cdot \frac{3}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine $- 3$ and $\frac{3}{3}$ .

$x = \frac{- \frac{11 z}{3} + \frac{- 3 \cdot 3}{3} + \frac{5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$x = \frac{- \frac{11 z}{3} + \frac{- 3 \cdot 3 + 5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$x = \frac{- \frac{11 z}{3} + \frac{- 9 + 5}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Add $- 9$ and $5$ .

$x = \frac{- \frac{11 z}{3} + \frac{- 4}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- \frac{11 z}{3} + \frac{- 4}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Move the negative in front of the fraction.

$x = \frac{- \frac{11 z}{3} - \frac{4}{3} - 3 z}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

To write $- 3 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{- \frac{11 z}{3} - 3 z \cdot \frac{3}{3} - \frac{4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine $- 3 z$ and $\frac{3}{3}$ .

$x = \frac{- \frac{11 z}{3} + \frac{- 3 z \cdot 3}{3} - \frac{4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$x = \frac{\frac{- 11 z - 3 z \cdot 3}{3} - \frac{4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Combine the numerators over the common denominator.

$x = \frac{\frac{- 11 z - 3 z \cdot 3 - 4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Multiply $3$ by $- 3$ .

$x = \frac{\frac{- 11 z - 9 z - 4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Subtract $9 z$ from $- 11 z$ .

$x = \frac{\frac{- 20 z - 4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $4$ out of $- 20 z - 4$ .

Factor $4$ out of $- 20 z$ .

$x = \frac{\frac{4 (- 5 z) - 4}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $4$ out of $- 4$ .

$x = \frac{\frac{4 (- 5 z) + 4 (- 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $4$ out of $4 (- 5 z) + 4 (- 1)$ .

$x = \frac{\frac{4 (- 5 z - 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{\frac{4 (- 5 z - 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $- 1$ out of $- 5 z$ .

$x = \frac{\frac{4 (- (5 z) - 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Rewrite $- 1$ as $- 1 (1)$ .

$x = \frac{\frac{4 (- (5 z) - 1 \cdot 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $- 1$ out of $- (5 z) - 1 (1)$ .

$x = \frac{\frac{4 (- (5 z + 1))}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the expression.

Rewrite $- (5 z + 1)$ as $- 1 (5 z + 1)$ .

$x = \frac{\frac{4 (- 1 (5 z + 1))}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Move the negative in front of the fraction.

$x = \frac{- \frac{4 (5 z + 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- \frac{4 (5 z + 1)}{3}}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{4 (5 z + 1)}{3} \cdot \frac{1}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4 (5 z + 1)}{3}$ into the numerator.

$x = \frac{- 4 (5 z + 1)}{3} \cdot \frac{1}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Factor $4$ out of $- 4 (5 z + 1)$ .

$x = \frac{4 (- (5 z + 1))}{3} \cdot \frac{1}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Cancel the common factor.

$x = \frac{4 (- (5 z + 1))}{3} \cdot \frac{1}{4}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Rewrite the expression.

$x = \frac{- (5 z + 1)}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = \frac{- (5 z + 1)}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Move the negative in front of the fraction.

$x = - \frac{5 z + 1}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{5 z + 1}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{5 z + 1}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{5 z + 1}{3}$

$\frac{25 z - 19}{6} = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Step 5

Solve for $z$ in $\frac{25 z - 19}{6} = 1$ .

Multiply both sides by $6$ .

$\frac{25 z - 19}{6} \cdot 6 = 1 \cdot 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{25 z - 19}{6} \cdot 6 = 1 \cdot 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Rewrite the expression.

$25 z - 19 = 1 \cdot 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$25 z - 19 = 1 \cdot 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$25 z - 19 = 1 \cdot 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the right side.

Multiply $6$ by $1$ .

$25 z - 19 = 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$25 z - 19 = 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$25 z - 19 = 6$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Solve for $z$ .

Move all terms not containing $z$ to the right side of the equation.

Add $19$ to both sides of the equation.

$25 z = 6 + 19$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Add $6$ and $19$ .

$25 z = 25$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$25 z = 25$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Divide each term in $25 z = 25$ by $25$ and simplify.

Divide each term in $25 z = 25$ by $25$ .

$\frac{25 z}{25} = \frac{25}{25}$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 z}{25} = \frac{25}{25}$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Divide $z$ by $1$ .

$z = \frac{25}{25}$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = \frac{25}{25}$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = \frac{25}{25}$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the right side.

Divide $25$ by $25$ .

$z = 1$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = 1$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = 1$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = 1$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$z = 1$

$x = - \frac{5 z + 1}{3}$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Step 6

Replace all occurrences of $z$ with $1$ in each equation.

Replace all occurrences of $z$ in $x = - \frac{5 z + 1}{3}$ with $1$ .

$x = - \frac{5 (1) + 1}{3}$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the right side.

Simplify $- \frac{5 (1) + 1}{3}$ .

Simplify the numerator.

Multiply $5$ by $1$ .

$x = - \frac{5 + 1}{3}$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Add $5$ and $1$ .

$x = - \frac{6}{3}$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - \frac{6}{3}$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Simplify the expression.

Divide $6$ by $3$ .

$x = - 1 \cdot 2$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Multiply $- 1$ by $2$ .

$x = - 2$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - 2$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - 2$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

$x = - 2$

$z = 1$

$y = - \frac{11 z}{6} + \frac{5}{6}$

Replace all occurrences of $z$ in $y = - \frac{11 z}{6} + \frac{5}{6}$ with $1$ .

$y = - \frac{11 (1)}{6} + \frac{5}{6}$

$x = - 2$

$z = 1$

Simplify the right side.

Simplify $- \frac{11 (1)}{6} + \frac{5}{6}$ .

Combine the numerators over the common denominator.

$y = \frac{- 11 \cdot 1 + 5}{6}$

$x = - 2$

$z = 1$

Simplify the expression.

Multiply $- 11$ by $1$ .

$y = \frac{- 11 + 5}{6}$

$x = - 2$

$z = 1$

Add $- 11$ and $5$ .

$y = \frac{- 6}{6}$

$x = - 2$

$z = 1$

Divide $- 6$ by $6$ .

$y = - 1$

$x = - 2$

$z = 1$

$y = - 1$

$x = - 2$

$z = 1$

$y = - 1$

$x = - 2$

$z = 1$

$y = - 1$

$x = - 2$

$z = 1$

$y = - 1$

$x = - 2$

$z = 1$

Step 7

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 2, - 1, 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1, 1)$

Equation Form:

$x = - 2, y = - 1, z = 1$

Solve the System of Equations 4x-2y+3z=-3 2x-3y+2z=1 6x+10z=-2

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