Solve the System of Equations 2x+4y+3z=6 5x+8y+6z=4 4x+5y+2z=6

$2 x + 4 y + 3 z = 6$ $5 x + 8 y + 6 z = 4$ $4 x + 5 y + 2 z = 6$

Solve for $x$ in $2 x + 4 y + 3 z = 6$ .

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

Subtract $4 y$ from both sides of the equation.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$2 x = 6 - 4 y - 3 z$

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

$2 x = 6 - 4 y - 3 z$

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Divide each term in $2 x = 6 - 4 y - 3 z$ by $2$ and simplify.

Divide each term in $2 x = 6 - 4 y - 3 z$ by $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Divide $x$ by $1$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

Factor $2$ out of $- 4 y$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Cancel the common factor.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Rewrite the expression.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Divide $- 2 y$ by $1$ .

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

Move the negative in front of the fraction.

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

$5 x + 8 y + 6 z = 4$

$4 x + 5 y + 2 z = 6$

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

Replace all occurrences of $x$ in $5 x + 8 y + 6 z = 4$ with $3 - 2 y - \frac{3 z}{2}$ .

$5 (3 - 2 y - \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Simplify the left side.

Simplify $5 (3 - 2 y - \frac{3 z}{2}) + 8 y + 6 z$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 3 + 5 (- 2 y) + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Simplify.

Multiply $5$ by $3$ .

$15 + 5 (- 2 y) + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Multiply $- 2$ by $5$ .

$15 - 10 y + 5 (- \frac{3 z}{2}) + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Multiply $5 (- \frac{3 z}{2})$ .

Multiply $- 1$ by $5$ .

$15 - 10 y - 5 \frac{3 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

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

$15 - 10 y + \frac{- 5 (3 z)}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Multiply $3$ by $- 5$ .

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y + \frac{- 15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Move the negative in front of the fraction.

$15 - 10 y - \frac{15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 10 y - \frac{15 z}{2} + 8 y + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

Add $- 10 y$ and $8 y$ .

$15 - 2 y - \frac{15 z}{2} + 6 z = 4$

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

$4 x + 5 y + 2 z = 6$

To write $6 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$15 - 2 y - \frac{15 z}{2} + 6 z \cdot \frac{2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Simplify terms.

Combine $6 z$ and $\frac{2}{2}$ .

$15 - 2 y - \frac{15 z}{2} + \frac{6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Combine the numerators over the common denominator.

$15 - 2 y + \frac{- 15 z + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{- 15 z + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Simplify each term.

Simplify the numerator.

Factor $3 z$ out of $- 15 z + 6 z \cdot 2$ .

Factor $3 z$ out of $- 15 z$ .

$15 - 2 y + \frac{3 z (- 5) + 6 z \cdot 2}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Factor $3 z$ out of $6 z \cdot 2$ .

$15 - 2 y + \frac{3 z (- 5) + 3 z (2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Factor $3 z$ out of $3 z (- 5) + 3 z (2 \cdot 2)$ .

$15 - 2 y + \frac{3 z (- 5 + 2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{3 z (- 5 + 2 \cdot 2)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Multiply $2$ by $2$ .

$15 - 2 y + \frac{3 z (- 5 + 4)}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Add $- 5$ and $4$ .

$15 - 2 y + \frac{3 z \cdot - 1}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Multiply $- 1$ by $3$ .

$15 - 2 y + \frac{- 3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y + \frac{- 3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

Move the negative in front of the fraction.

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$4 x + 5 y + 2 z = 6$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Simplify.

Multiply $4$ by $3$ .

$12 + 4 (- 2 y) + 4 (- \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Multiply $- 2$ by $4$ .

$12 - 8 y + 4 (- \frac{3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 z}{2}$ into the numerator.

$12 - 8 y + 4 (\frac{- 3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Factor $2$ out of $4$ .

$12 - 8 y + 2 (2) (\frac{- 3 z}{2}) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Cancel the common factor.

$12 - 8 y + 2 \cdot (2 (\frac{- 3 z}{2})) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Rewrite the expression.

$12 - 8 y + 2 (- 3 z) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y + 2 (- 3 z) + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Multiply $- 3$ by $2$ .

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 8 y - 6 z + 5 y + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Simplify by adding terms.

Add $- 8 y$ and $5 y$ .

$12 - 3 y - 6 z + 2 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Add $- 6 z$ and $2 z$ .

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$12 - 3 y - 4 z = 6$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Solve for $y$ in $12 - 3 y - 4 z = 6$ .

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

Subtract $12$ from both sides of the equation.

$- 3 y - 4 z = 6 - 12$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Add $4 z$ to both sides of the equation.

$- 3 y = 6 - 12 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Subtract $12$ from $6$ .

$- 3 y = - 6 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$- 3 y = - 6 + 4 z$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Divide each term in $- 3 y = - 6 + 4 z$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6 + 4 z$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{4 z}{- 3}$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{4 z}{- 3}$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3} + \frac{4 z}{- 3}$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$y = \frac{- 6}{- 3} + \frac{4 z}{- 3}$

$15 - 2 y - \frac{3 z}{2} = 4$

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

$y = \frac{- 6}{- 3} + \frac{4 z}{- 3}$

$15 - 2 y - \frac{3 z}{2} = 4$

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

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 3$ .

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

Move the negative in front of the fraction.

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

$15 - 2 y - \frac{3 z}{2} = 4$

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

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

Replace all occurrences of $y$ in $15 - 2 y - \frac{3 z}{2} = 4$ with $2 - \frac{4 z}{3}$ .

$15 - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Simplify the left side.

Simplify $15 - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2}$ .

Find the common denominator.

Write $15$ as a fraction with denominator $1$ .

$\frac{15}{1} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Multiply $\frac{15}{1}$ by $\frac{2}{2}$ .

$\frac{15}{1} \cdot \frac{2}{2} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Multiply $\frac{15}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} - 2 (2 - \frac{4 z}{3}) - \frac{3 z}{2} = 4$

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

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

Write $- 2 (2 - \frac{4 z}{3})$ as a fraction with denominator $1$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3})}{1} - \frac{3 z}{2} = 4$

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

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

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3})}{1} \cdot \frac{2}{2} - \frac{3 z}{2} = 4$

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

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

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3}) \cdot 2}{2} - \frac{3 z}{2} = 4$

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

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

$\frac{15 \cdot 2}{2} + \frac{- 2 (2 - \frac{4 z}{3}) \cdot 2}{2} - \frac{3 z}{2} = 4$

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

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

Combine the numerators over the common denominator.

$\frac{15 \cdot 2 - 2 (2 - \frac{4 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Simplify each term.

Multiply $15$ by $2$ .

$\frac{30 - 2 (2 - \frac{4 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Apply the distributive property.

$\frac{30 + (- 2 \cdot 2 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Multiply $- 2$ by $2$ .

$\frac{30 + (- 4 - 2 (- \frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Multiply $- 2 (- \frac{4 z}{3})$ .

Multiply $- 1$ by $- 2$ .

$\frac{30 + (- 4 + 2 (\frac{4 z}{3})) \cdot 2 - 3 z}{2} = 4$

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

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

Combine $2$ and $\frac{4 z}{3}$ .

$\frac{30 + (- 4 + \frac{2 (4 z)}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Multiply $4$ by $2$ .

$\frac{30 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

$\frac{30 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2} = 4$

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

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

Apply the distributive property.

$\frac{30 - 4 \cdot 2 + \frac{8 z}{3} \cdot 2 - 3 z}{2} = 4$

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

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

Multiply $- 4$ by $2$ .

$\frac{30 - 8 + \frac{8 z}{3} \cdot 2 - 3 z}{2} = 4$

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

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

Multiply $\frac{8 z}{3} \cdot 2$ .

Combine $\frac{8 z}{3}$ and $2$ .

$\frac{30 - 8 + \frac{8 z \cdot 2}{3} - 3 z}{2} = 4$

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

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

Multiply $2$ by $8$ .

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

$\frac{30 - 8 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

Subtract $8$ from $30$ .

$\frac{22 + \frac{16 z}{3} - 3 z}{2} = 4$

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

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

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

$\frac{22 + \frac{16 z}{3} - 3 z \cdot \frac{3}{3}}{2} = 4$

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

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

Simplify terms.

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

$\frac{22 + \frac{16 z}{3} + \frac{- 3 z \cdot 3}{3}}{2} = 4$

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

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

Combine the numerators over the common denominator.

$\frac{22 + \frac{16 z - 3 z \cdot 3}{3}}{2} = 4$

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

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

Simplify each term.

Simplify the numerator.

Factor $z$ out of $16 z - 3 z \cdot 3$ .

Factor $z$ out of $16 z$ .

$\frac{22 + \frac{z \cdot 16 - 3 z \cdot 3}{3}}{2} = 4$

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

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

Factor $z$ out of $- 3 z \cdot 3$ .

$\frac{22 + \frac{z \cdot 16 + z (- 3 \cdot 3)}{3}}{2} = 4$

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

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

Factor $z$ out of $z \cdot 16 + z (- 3 \cdot 3)$ .

$\frac{22 + \frac{z (16 - 3 \cdot 3)}{3}}{2} = 4$

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

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

$\frac{22 + \frac{z (16 - 3 \cdot 3)}{3}}{2} = 4$

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

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

Multiply $- 3$ by $3$ .

$\frac{22 + \frac{z (16 - 9)}{3}}{2} = 4$

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

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

Subtract $9$ from $16$ .

$\frac{22 + \frac{z \cdot 7}{3}}{2} = 4$

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

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

$\frac{22 + \frac{z \cdot 7}{3}}{2} = 4$

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

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

Move $7$ to the left of $z$ .

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

$\frac{22 + \frac{7 z}{3}}{2} = 4$

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

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

Simplify the numerator.

To write $22$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{22 \cdot \frac{3}{3} + \frac{7 z}{3}}{2} = 4$

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

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

Combine $22$ and $\frac{3}{3}$ .

$\frac{\frac{22 \cdot 3}{3} + \frac{7 z}{3}}{2} = 4$

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

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

Combine the numerators over the common denominator.

$\frac{\frac{22 \cdot 3 + 7 z}{3}}{2} = 4$

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

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

Multiply $22$ by $3$ .

$\frac{\frac{66 + 7 z}{3}}{2} = 4$

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

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

$\frac{\frac{66 + 7 z}{3}}{2} = 4$

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

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

Multiply the numerator by the reciprocal of the denominator.

$\frac{66 + 7 z}{3} \cdot \frac{1}{2} = 4$

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

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

Multiply $\frac{66 + 7 z}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{66 + 7 z}{3}$ by $\frac{1}{2}$ .

$\frac{66 + 7 z}{3 \cdot 2} = 4$

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

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

Multiply $3$ by $2$ .

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

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

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

$\frac{66 + 7 z}{6} = 4$

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

Simplify the right side.

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

Find the common denominator.

Write $3$ as a fraction with denominator $1$ .

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

$\frac{66 + 7 z}{6} = 4$

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

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

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

$\frac{66 + 7 z}{6} = 4$

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

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

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

$\frac{66 + 7 z}{6} = 4$

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

Write $- 2 (2 - \frac{4 z}{3})$ as a fraction with denominator $1$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Multiply $\frac{- 2 (2 - \frac{4 z}{3})}{1}$ by $\frac{2}{2}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

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

$\frac{66 + 7 z}{6} = 4$

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

Combine the numerators over the common denominator.

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

$\frac{66 + 7 z}{6} = 4$

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

Simplify each term.

Multiply $3$ by $2$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Apply the distributive property.

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

$\frac{66 + 7 z}{6} = 4$

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

Multiply $- 2$ by $2$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Multiply $- 2 (- \frac{4 z}{3})$ .

Multiply $- 1$ by $- 2$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Combine $2$ and $\frac{4 z}{3}$ .

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

$\frac{66 + 7 z}{6} = 4$

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

Multiply $4$ by $2$ .

$x = \frac{6 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 + (- 4 + \frac{8 z}{3}) \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Apply the distributive property.

$x = \frac{6 - 4 \cdot 2 + \frac{8 z}{3} \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $- 4$ by $2$ .

$x = \frac{6 - 8 + \frac{8 z}{3} \cdot 2 - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $\frac{8 z}{3} \cdot 2$ .

Combine $\frac{8 z}{3}$ and $2$ .

$x = \frac{6 - 8 + \frac{8 z \cdot 2}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $2$ by $8$ .

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{6 - 8 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Subtract $8$ from $6$ .

$x = \frac{- 2 + \frac{16 z}{3} - 3 z}{2}$

$\frac{66 + 7 z}{6} = 4$

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

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

$x = \frac{- 2 + \frac{16 z}{3} - 3 z \cdot \frac{3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Simplify terms.

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

$x = \frac{- 2 + \frac{16 z}{3} + \frac{- 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Combine the numerators over the common denominator.

$x = \frac{- 2 + \frac{16 z - 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Simplify each term.

Simplify the numerator.

Factor $z$ out of $16 z - 3 z \cdot 3$ .

Factor $z$ out of $16 z$ .

$x = \frac{- 2 + \frac{z \cdot 16 - 3 z \cdot 3}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Factor $z$ out of $- 3 z \cdot 3$ .

$x = \frac{- 2 + \frac{z \cdot 16 + z (- 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Factor $z$ out of $z \cdot 16 + z (- 3 \cdot 3)$ .

$x = \frac{- 2 + \frac{z (16 - 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{z (16 - 3 \cdot 3)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $- 3$ by $3$ .

$x = \frac{- 2 + \frac{z (16 - 9)}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Subtract $9$ from $16$ .

$x = \frac{- 2 + \frac{z \cdot 7}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{z \cdot 7}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Move $7$ to the left of $z$ .

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 2 + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Simplify the numerator.

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

$x = \frac{- 2 \cdot \frac{3}{3} + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

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

$x = \frac{\frac{- 2 \cdot 3}{3} + \frac{7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Combine the numerators over the common denominator.

$x = \frac{\frac{- 2 \cdot 3 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $- 2$ by $3$ .

$x = \frac{\frac{- 6 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{\frac{- 6 + 7 z}{3}}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{- 6 + 7 z}{3} \cdot \frac{1}{2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $\frac{- 6 + 7 z}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{- 6 + 7 z}{3}$ by $\frac{1}{2}$ .

$x = \frac{- 6 + 7 z}{3 \cdot 2}$

$\frac{66 + 7 z}{6} = 4$

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

Multiply $3$ by $2$ .

$x = \frac{- 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = \frac{- 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Rewrite $- 6$ as $- 1 (6)$ .

$x = \frac{- 1 \cdot 6 + 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Factor $- 1$ out of $7 z$ .

$x = \frac{- 1 \cdot 6 - (- 7 z)}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Factor $- 1$ out of $- 1 (6) - (- 7 z)$ .

$x = \frac{- 1 (6 - 7 z)}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Move the negative in front of the fraction.

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

$x = - \frac{6 - 7 z}{6}$

$\frac{66 + 7 z}{6} = 4$

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

Solve for $z$ in $\frac{66 + 7 z}{6} = 4$ .

Multiply both sides by $6$ .

$\frac{66 + 7 z}{6} \cdot 6 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Simplify.

Simplify the left side.

Simplify $\frac{66 + 7 z}{6} \cdot 6$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{66 + 7 z}{6} \cdot 6 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Rewrite the expression.

$66 + 7 z = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$66 + 7 z = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Reorder $66$ and $7 z$ .

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 4 \cdot 6$

$x = - \frac{6 - 7 z}{6}$

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

Simplify the right side.

Multiply $4$ by $6$ .

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

$7 z + 66 = 24$

$x = - \frac{6 - 7 z}{6}$

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

Solve for $z$ .

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

Subtract $66$ from both sides of the equation.

$7 z = 24 - 66$

$x = - \frac{6 - 7 z}{6}$

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

Subtract $66$ from $24$ .

$7 z = - 42$

$x = - \frac{6 - 7 z}{6}$

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

$7 z = - 42$

$x = - \frac{6 - 7 z}{6}$

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

Divide each term in $7 z = - 42$ by $7$ and simplify.

Divide each term in $7 z = - 42$ by $7$ .

$\frac{7 z}{7} = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 z}{7} = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Divide $z$ by $1$ .

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

$z = \frac{- 42}{7}$

$x = - \frac{6 - 7 z}{6}$

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

Simplify the right side.

Divide $- 42$ by $7$ .

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

$z = - 6$

$x = - \frac{6 - 7 z}{6}$

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

Replace all occurrences of $z$ with $- 6$ in each equation.

Replace all occurrences of $z$ in $x = - \frac{6 - 7 z}{6}$ with $- 6$ .

$x = - \frac{6 - 7 \cdot - 6}{6}$

$z = - 6$

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

Simplify the right side.

Simplify $- \frac{6 - 7 \cdot - 6}{6}$ .

Cancel the common factor of $6 - 7 \cdot - 6$ and $6$ .

Rewrite $6$ as $- 1 (- 6)$ .

$x = - \frac{- 1 \cdot - 6 - 7 \cdot - 6}{6}$

$z = - 6$

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

Factor $- 1$ out of $- 7 \cdot - 6$ .

$x = - \frac{- 1 \cdot - 6 - (7 \cdot - 6)}{6}$

$z = - 6$

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

Factor $- 1$ out of $- 1 (- 6) - (7 \cdot - 6)$ .

$x = - \frac{- 1 (- 6 + 7 \cdot - 6)}{6}$

$z = - 6$

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

Reorder terms.

$x = - \frac{- 1 (- 6 - 6 \cdot 7)}{6}$

$z = - 6$

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

Factor $6$ out of $- 1 (- 6 - 6 \cdot 7)$ .

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6}$

$z = - 6$

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

Cancel the common factors.

Factor $6$ out of $6$ .

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6 (1)}$

$z = - 6$

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

Cancel the common factor.

$x = - \frac{6 (- 1 (- 1 - 1 \cdot 7))}{6 \cdot 1}$

$z = - 6$

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

Rewrite the expression.

$x = - \frac{- 1 (- 1 - 1 \cdot 7)}{1}$

$z = - 6$

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

Divide $- 1 (- 1 - 1 \cdot 7)$ by $1$ .

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

$x = - (- 1 (- 1 - 1 \cdot 7))$

$z = - 6$

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

Simplify the expression.

Rewrite $- 1 (- 1 - 1 \cdot 7)$ as $- (- 1 - 1 \cdot 7)$ .

$x = - 1 - 1 \cdot 7$

$z = - 6$

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

Multiply $- 1$ by $7$ .

$x = - 1 - 7$

$z = - 6$

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

Subtract $7$ from $- 1$ .

$x = - 8$

$z = - 6$

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

Multiply $- 1$ by $- 8$ .

$x = - 1 \cdot 8$

$z = - 6$

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

Multiply $- 1$ by $8$ .

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

$x = - 8$

$z = - 6$

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

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

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

$x = - 8$

$z = - 6$

Simplify the right side.

Simplify $2 - \frac{4 (- 6)}{3}$ .

Simplify each term.

Cancel the common factor of $- 6$ and $3$ .

Factor $3$ out of $4 (- 6)$ .

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

$x = - 8$

$z = - 6$

Cancel the common factors.

Factor $3$ out of $3$ .

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

$x = - 8$

$z = - 6$

Cancel the common factor.

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

$x = - 8$

$z = - 6$

Rewrite the expression.

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

$x = - 8$

$z = - 6$

Divide $4 \cdot (- 2)$ by $1$ .

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

$y = 2 - (4 \cdot (- 2))$

$x = - 8$

$z = - 6$

Multiply $4$ by $- 2$ .

$y = 2 + 8$

$x = - 8$

$z = - 6$

Multiply $- 1$ by $- 8$ .

$y = 2 + 8$

$x = - 8$

$z = - 6$

$y = 2 + 8$

$x = - 8$

$z = - 6$

Add $2$ and $8$ .

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

$y = 10$

$x = - 8$

$z = - 6$

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

$(- 8, 10, - 6)$

The result can be shown in multiple forms.

Point Form:

$(- 8, 10, - 6)$

Equation Form:

$x = - 8, y = 10, z = - 6$

Solve the System of Equations 2x+4y+3z=6 5x+8y+6z=4 4x+5y+2z=6

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