Solve the System of Equations 2x+y=1 -2y+5z=-5 3x+4z=-2

$2 x + y = 1$ $- 2 y + 5 z = - 5$ $3 x + 4 z = - 2$

Subtract $2 x$ from both sides of the equation.

$y = 1 - 2 x$

$- 2 y + 5 z = - 5$

$3 x + 4 z = - 2$

Replace all occurrences of $y$ with $1 - 2 x$ in each equation.

Replace all occurrences of $y$ in $- 2 y + 5 z = - 5$ with $1 - 2 x$ .

$- 2 (1 - 2 x) + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$- 2 \cdot 1 - 2 (- 2 x) + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

Multiply $- 2$ by $1$ .

$- 2 - 2 (- 2 x) + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

Multiply $- 2$ by $- 2$ .

$- 2 + 4 x + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

$- 2 + 4 x + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

$- 2 + 4 x + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

$- 2 + 4 x + 5 z = - 5$

$y = 1 - 2 x$

$3 x + 4 z = - 2$

Reorder $1$ and $- 2 x$ .

$y = - 2 x + 1$

$- 2 + 4 x + 5 z = - 5$

$3 x + 4 z = - 2$

Solve for $x$ in $- 2 + 4 x + 5 z = - 5$ .

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

Add $2$ to both sides of the equation.

$4 x + 5 z = - 5 + 2$

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Subtract $5 z$ from both sides of the equation.

$4 x = - 5 + 2 - 5 z$

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Add $- 5$ and $2$ .

$4 x = - 3 - 5 z$

$y = - 2 x + 1$

$3 x + 4 z = - 2$

$4 x = - 3 - 5 z$

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Divide each term in $4 x = - 3 - 5 z$ by $4$ and simplify.

Divide each term in $4 x = - 3 - 5 z$ by $4$ .

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Divide $x$ by $1$ .

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Move the negative in front of the fraction.

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

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

$y = - 2 x + 1$

$3 x + 4 z = - 2$

Replace all occurrences of $x$ with $- \frac{3}{4} - \frac{5 z}{4}$ in each equation.

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

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

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

$3 x + 4 z = - 2$

Simplify the right side.

Simplify $- 2 (- \frac{3}{4} - \frac{5 z}{4}) + 1$ .

Simplify each term.

Apply the distributive property.

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

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

$3 x + 4 z = - 2$

Cancel the common factor of $2$ .

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

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

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

$3 x + 4 z = - 2$

Factor $2$ out of $- 2$ .

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

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

$3 x + 4 z = - 2$

Factor $2$ out of $4$ .

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

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

$3 x + 4 z = - 2$

Cancel the common factor.

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

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

$3 x + 4 z = - 2$

Rewrite the expression.

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

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

$3 x + 4 z = - 2$

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

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

$3 x + 4 z = - 2$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 z}{4}$ into the numerator.

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

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

$3 x + 4 z = - 2$

Factor $2$ out of $- 2$ .

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

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

$3 x + 4 z = - 2$

Factor $2$ out of $4$ .

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

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

$3 x + 4 z = - 2$

Cancel the common factor.

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

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

$3 x + 4 z = - 2$

Rewrite the expression.

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

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

$3 x + 4 z = - 2$

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

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

$3 x + 4 z = - 2$

Simplify each term.

Move the negative in front of the fraction.

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

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

$3 x + 4 z = - 2$

Multiply $- 1 (- \frac{3}{2})$ .

Multiply $- 1$ by $- 1$ .

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

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

$3 x + 4 z = - 2$

Multiply $\frac{3}{2}$ by $1$ .

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

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

$3 x + 4 z = - 2$

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

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

$3 x + 4 z = - 2$

Move the negative in front of the fraction.

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

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

$3 x + 4 z = - 2$

Multiply $- 1 (- \frac{5 z}{2})$ .

Multiply $- 1$ by $- 1$ .

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

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

$3 x + 4 z = - 2$

Multiply $\frac{5 z}{2}$ by $1$ .

$y = \frac{3}{2} + \frac{5 z}{2} + 1$

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

$3 x + 4 z = - 2$

$y = \frac{3}{2} + \frac{5 z}{2} + 1$

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

$3 x + 4 z = - 2$

$y = \frac{3}{2} + \frac{5 z}{2} + 1$

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

$3 x + 4 z = - 2$

$y = \frac{3}{2} + \frac{5 z}{2} + 1$

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

$3 x + 4 z = - 2$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$y = \frac{5 z}{2} + \frac{3}{2} + \frac{2}{2}$

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

$3 x + 4 z = - 2$

Combine the numerators over the common denominator.

$y = \frac{5 z}{2} + \frac{3 + 2}{2}$

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

$3 x + 4 z = - 2$

Add $3$ and $2$ .

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$3 x + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$3 x + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$3 x + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$3 x + 4 z = - 2$

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

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

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $3 (- \frac{3}{4})$ .

Multiply $- 1$ by $3$ .

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

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Combine $- 3$ and $\frac{3}{4}$ .

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

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $- 3$ by $3$ .

$\frac{- 9}{4} + 3 (- \frac{5 z}{4}) + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$\frac{- 9}{4} + 3 (- \frac{5 z}{4}) + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $3 (- \frac{5 z}{4})$ .

Multiply $- 1$ by $3$ .

$\frac{- 9}{4} - 3 \frac{5 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Combine $- 3$ and $\frac{5 z}{4}$ .

$\frac{- 9}{4} + \frac{- 3 (5 z)}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $5$ by $- 3$ .

$\frac{- 9}{4} + \frac{- 15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$\frac{- 9}{4} + \frac{- 15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify each term.

Move the negative in front of the fraction.

$- \frac{9}{4} + \frac{- 15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Move the negative in front of the fraction.

$- \frac{9}{4} - \frac{15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- \frac{9}{4} - \frac{15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- \frac{9}{4} - \frac{15 z}{4} + 4 z = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

To write $4 z$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{9}{4} - \frac{15 z}{4} + 4 z \cdot \frac{4}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Combine $4 z$ and $\frac{4}{4}$ .

$- \frac{9}{4} - \frac{15 z}{4} + \frac{4 z \cdot 4}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Combine the numerators over the common denominator.

$- \frac{9}{4} + \frac{- 15 z + 4 z \cdot 4}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Combine the numerators over the common denominator.

$\frac{- 9 - 15 z + 4 z \cdot 4}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $4$ by $4$ .

$\frac{- 9 - 15 z + 16 z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Add $- 15 z$ and $16 z$ .

$\frac{- 9 + z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 \cdot 9 + z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Factor $- 1$ out of $z$ .

$\frac{- 1 \cdot 9 - 1 (- z)}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Factor $- 1$ out of $- 1 (9) - 1 (- z)$ .

$\frac{- 1 (9 - z)}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Move the negative in front of the fraction.

$- \frac{9 - z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- \frac{9 - z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- \frac{9 - z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- \frac{9 - z}{4} = - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Solve for $z$ in $- \frac{9 - z}{4} = - 2$ .

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{9 - z}{4}) = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{9 - z}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{9 - z}{4}$ into the numerator.

$- 4 \frac{- (9 - z)}{4} = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Factor $4$ out of $- 4$ .

$4 (- 1) (\frac{- (9 - z)}{4}) = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Cancel the common factor.

$4 \cdot (- 1 \frac{- (9 - z)}{4}) = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Rewrite the expression.

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (9 - z) = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Multiply $9 - z$ by $1$ .

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = - 4 \cdot - 2$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify the right side.

Multiply $- 4$ by $- 2$ .

$9 - z = 8$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = 8$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$9 - z = 8$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

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

Subtract $9$ from both sides of the equation.

$- z = 8 - 9$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Subtract $9$ from $8$ .

$- z = - 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$- z = - 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Divide each term in $- z = - 1$ by $- 1$ and simplify.

Divide each term in $- z = - 1$ by $- 1$ .

$\frac{- z}{- 1} = \frac{- 1}{- 1}$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{- 1}{- 1}$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Divide $z$ by $1$ .

$z = \frac{- 1}{- 1}$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$z = \frac{- 1}{- 1}$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$z = 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$z = 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$z = 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

$z = 1$

$y = \frac{5 z}{2} + \frac{5}{2}$

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

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

Replace all occurrences of $z$ in $y = \frac{5 z}{2} + \frac{5}{2}$ with $1$ .

$y = \frac{5 (1)}{2} + \frac{5}{2}$

$z = 1$

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

Simplify the right side.

Simplify $\frac{5 (1)}{2} + \frac{5}{2}$ .

Combine the numerators over the common denominator.

$y = \frac{5 (1) + 5}{2}$

$z = 1$

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

Simplify the expression.

Multiply $5$ by $1$ .

$y = \frac{5 + 5}{2}$

$z = 1$

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

Add $5$ and $5$ .

$y = \frac{10}{2}$

$z = 1$

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

Divide $10$ by $2$ .

$y = 5$

$z = 1$

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

$y = 5$

$z = 1$

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

$y = 5$

$z = 1$

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

$y = 5$

$z = 1$

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

Replace all occurrences of $z$ in $x = - \frac{3}{4} - \frac{5 z}{4}$ with $1$ .

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

$y = 5$

$z = 1$

Simplify the right side.

Simplify $- \frac{3}{4} - \frac{5 (1)}{4}$ .

Combine the numerators over the common denominator.

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

$y = 5$

$z = 1$

Simplify the expression.

Multiply $- 5$ by $1$ .

$x = \frac{- 3 - 5}{4}$

$y = 5$

$z = 1$

Subtract $5$ from $- 3$ .

$x = \frac{- 8}{4}$

$y = 5$

$z = 1$

Divide $- 8$ by $4$ .

$x = - 2$

$y = 5$

$z = 1$

$x = - 2$

$y = 5$

$z = 1$

$x = - 2$

$y = 5$

$z = 1$

$x = - 2$

$y = 5$

$z = 1$

$x = - 2$

$y = 5$

$z = 1$

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

$(- 2, 5, 1)$

The result can be shown in multiple forms.

Point Form:

$(- 2, 5, 1)$

Equation Form:

$x = - 2, y = 5, z = 1$

Solve the System of Equations 2x+y=1 -2y+5z=-5 3x+4z=-2

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