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

$x + 2 y - 4 z = 4$ $2 x - y + 2 z = 3$ $3 x - 8 z = - 2$

Step 1

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

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

$x - 4 z = 4 - 2 y$

$2 x - y + 2 z = 3$

$3 x - 8 z = - 2$

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

$x = 4 - 2 y + 4 z$

$2 x - y + 2 z = 3$

$3 x - 8 z = - 2$

$x = 4 - 2 y + 4 z$

$2 x - y + 2 z = 3$

$3 x - 8 z = - 2$

Step 2

Replace all occurrences of $x$ with $4 - 2 y + 4 z$ in each equation.

Replace all occurrences of $x$ in $2 x - y + 2 z = 3$ with $4 - 2 y + 4 z$ .

$2 (4 - 2 y + 4 z) - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Simplify the left side.

Simplify $2 (4 - 2 y + 4 z) - y + 2 z$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 4 + 2 (- 2 y) + 2 (4 z) - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Simplify.

Multiply $2$ by $4$ .

$8 + 2 (- 2 y) + 2 (4 z) - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Multiply $- 2$ by $2$ .

$8 - 4 y + 2 (4 z) - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Multiply $4$ by $2$ .

$8 - 4 y + 8 z - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

$8 - 4 y + 8 z - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

$8 - 4 y + 8 z - y + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Simplify by adding terms.

Subtract $y$ from $- 4 y$ .

$8 - 5 y + 8 z + 2 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Add $8 z$ and $2 z$ .

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$3 x - 8 z = - 2$

Replace all occurrences of $x$ in $3 x - 8 z = - 2$ with $4 - 2 y + 4 z$ .

$3 (4 - 2 y + 4 z) - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Simplify the left side.

Simplify $3 (4 - 2 y + 4 z) - 8 z$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 4 + 3 (- 2 y) + 3 (4 z) - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Simplify.

Multiply $3$ by $4$ .

$12 + 3 (- 2 y) + 3 (4 z) - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Multiply $- 2$ by $3$ .

$12 - 6 y + 3 (4 z) - 8 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Multiply $4$ by $3$ .

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

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

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

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

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

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Subtract $8 z$ from $12 z$ .

$12 - 6 y + 4 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$12 - 6 y + 4 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$12 - 6 y + 4 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$12 - 6 y + 4 z = - 2$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Step 3

Solve for $y$ in $12 - 6 y + 4 z = - 2$ .

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

Subtract $12$ from both sides of the equation.

$- 6 y + 4 z = - 2 - 12$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

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

$- 6 y = - 2 - 12 - 4 z$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Subtract $12$ from $- 2$ .

$- 6 y = - 14 - 4 z$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$- 6 y = - 14 - 4 z$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Divide each term in $- 6 y = - 14 - 4 z$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 14 - 4 z$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 14}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 14}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Divide $y$ by $1$ .

$y = \frac{- 14}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{- 14}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{- 14}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 14$ and $- 6$ .

Factor $- 2$ out of $- 14$ .

$y = \frac{- 2 \cdot 7}{- 6} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = \frac{- 2 \cdot 7}{- 2 \cdot 3} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Cancel the common factor.

$y = \frac{- 2 \cdot 7}{- 2 \cdot 3} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Rewrite the expression.

$y = \frac{7}{3} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{- 4 z}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Cancel the common factor of $- 4$ and $- 6$ .

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

$y = \frac{7}{3} + \frac{- 2 (2 z)}{- 6}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = \frac{7}{3} + \frac{- 2 (2 z)}{- 2 \cdot 3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Cancel the common factor.

$y = \frac{7}{3} + \frac{- 2 (2 z)}{- 2 \cdot 3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Rewrite the expression.

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

$y = \frac{7}{3} + \frac{2 z}{3}$

$8 - 5 y + 10 z = 3$

$x = 4 - 2 y + 4 z$

Step 4

Replace all occurrences of $y$ with $\frac{7}{3} + \frac{2 z}{3}$ in each equation.

Replace all occurrences of $y$ in $8 - 5 y + 10 z = 3$ with $\frac{7}{3} + \frac{2 z}{3}$ .

$8 - 5 (\frac{7}{3} + \frac{2 z}{3}) + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Simplify the left side.

Simplify $8 - 5 (\frac{7}{3} + \frac{2 z}{3}) + 10 z$ .

Simplify each term.

Apply the distributive property.

$8 - 5 (\frac{7}{3}) - 5 \frac{2 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Multiply $- 5 (\frac{7}{3})$ .

Combine $- 5$ and $\frac{7}{3}$ .

$8 + \frac{- 5 \cdot 7}{3} - 5 \frac{2 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Multiply $- 5$ by $7$ .

$8 + \frac{- 35}{3} - 5 \frac{2 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$8 + \frac{- 35}{3} - 5 \frac{2 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

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

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

$8 + \frac{- 35}{3} + \frac{- 5 (2 z)}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Multiply $2$ by $- 5$ .

$8 + \frac{- 35}{3} + \frac{- 10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$8 + \frac{- 35}{3} + \frac{- 10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Simplify each term.

Move the negative in front of the fraction.

$8 - \frac{35}{3} + \frac{- 10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Move the negative in front of the fraction.

$8 - \frac{35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$8 - \frac{35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$8 - \frac{35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$8 \cdot \frac{3}{3} - \frac{35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

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

$\frac{8 \cdot 3}{3} - \frac{35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 - 35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Simplify the numerator.

Multiply $8$ by $3$ .

$\frac{24 - 35}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Subtract $35$ from $24$ .

$\frac{- 11}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$\frac{- 11}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Move the negative in front of the fraction.

$- \frac{11}{3} - \frac{10 z}{3} + 10 z = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

To write $10 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{11}{3} - \frac{10 z}{3} + 10 z \cdot \frac{3}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Combine $10 z$ and $\frac{3}{3}$ .

$- \frac{11}{3} - \frac{10 z}{3} + \frac{10 z \cdot 3}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Combine the numerators over the common denominator.

$- \frac{11}{3} + \frac{- 10 z + 10 z \cdot 3}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Combine the numerators over the common denominator.

$\frac{- 11 - 10 z + 10 z \cdot 3}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Multiply $3$ by $10$ .

$\frac{- 11 - 10 z + 30 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Add $- 10 z$ and $30 z$ .

$\frac{- 11 + 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Rewrite $- 11$ as $- 1 (11)$ .

$\frac{- 1 \cdot 11 + 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Factor $- 1$ out of $20 z$ .

$\frac{- 1 \cdot 11 - (- 20 z)}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Factor $- 1$ out of $- 1 (11) - (- 20 z)$ .

$\frac{- 1 (11 - 20 z)}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Move the negative in front of the fraction.

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - 2 y + 4 z$

Replace all occurrences of $y$ in $x = 4 - 2 y + 4 z$ with $\frac{7}{3} + \frac{2 z}{3}$ .

$x = 4 - 2 (\frac{7}{3} + \frac{2 z}{3}) + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the right side.

Simplify $4 - 2 (\frac{7}{3} + \frac{2 z}{3}) + 4 z$ .

Simplify each term.

Apply the distributive property.

$x = 4 - 2 (\frac{7}{3}) - 2 \frac{2 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $- 2 (\frac{7}{3})$ .

Combine $- 2$ and $\frac{7}{3}$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $- 2$ by $7$ .

$x = 4 + \frac{- 14}{3} - 2 \frac{2 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 + \frac{- 14}{3} - 2 \frac{2 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $- 2 \frac{2 z}{3}$ .

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

$x = 4 + \frac{- 14}{3} + \frac{- 2 (2 z)}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $2$ by $- 2$ .

$x = 4 + \frac{- 14}{3} + \frac{- 4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 + \frac{- 14}{3} + \frac{- 4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify each term.

Move the negative in front of the fraction.

$x = 4 - \frac{14}{3} + \frac{- 4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Move the negative in front of the fraction.

$x = 4 - \frac{14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - \frac{14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 4 - \frac{14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 4 \cdot \frac{3}{3} - \frac{14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$x = \frac{4 \cdot 3}{3} - \frac{14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

$x = \frac{4 \cdot 3 - 14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$x = \frac{12 - 14}{3} - \frac{4 z}{3} + 4 z$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Subtract $14$ from $12$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Move the negative in front of the fraction.

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

To write $4 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Combine the numerators over the common denominator.

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $3$ by $4$ .

$x = \frac{- 2 - 4 z + 12 z}{3}$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Add $- 4 z$ and $12 z$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Factor $2$ out of $- 2 + 8 z$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1) + 8 z}{3}$

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Factor $2$ out of $8 z$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Factor $2$ out of $2 (- 1) + 2 (4 z)$ .

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Move the negative in front of the fraction.

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

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

$- \frac{11 - 20 z}{3} = 3$

$y = \frac{7}{3} + \frac{2 z}{3}$

Step 5

Solve for $z$ in $- \frac{11 - 20 z}{3} = 3$ .

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{11 - 20 z}{3}) = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{11 - 20 z}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{11 - 20 z}{3}$ into the numerator.

$- 3 \frac{- (11 - 20 z)}{3} = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Factor $3$ out of $- 3$ .

$3 (- 1) (\frac{- (11 - 20 z)}{3}) = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Cancel the common factor.

$3 \cdot (- 1 \frac{- (11 - 20 z)}{3}) = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Rewrite the expression.

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (11 - 20 z) = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $11 - 20 z$ by $1$ .

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 3 \cdot 3$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the right side.

Multiply $- 3$ by $3$ .

$11 - 20 z = - 9$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 9$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$11 - 20 z = - 9$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

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

Subtract $11$ from both sides of the equation.

$- 20 z = - 9 - 11$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Subtract $11$ from $- 9$ .

$- 20 z = - 20$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$- 20 z = - 20$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Divide each term in $- 20 z = - 20$ by $- 20$ and simplify.

Divide each term in $- 20 z = - 20$ by $- 20$ .

$\frac{- 20 z}{- 20} = \frac{- 20}{- 20}$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 z}{- 20} = \frac{- 20}{- 20}$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Divide $z$ by $1$ .

$z = \frac{- 20}{- 20}$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$z = \frac{- 20}{- 20}$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$z = \frac{- 20}{- 20}$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the right side.

Divide $- 20$ by $- 20$ .

$z = 1$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$z = 1$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$z = 1$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

$z = 1$

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

$y = \frac{7}{3} + \frac{2 z}{3}$

Step 6

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

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

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

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the right side.

Simplify $- \frac{2 (1 - 4 \cdot 1)}{3}$ .

Simplify the numerator.

Multiply $- 4$ by $1$ .

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

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Subtract $4$ from $1$ .

$x = - \frac{2 \cdot - 3}{3}$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = - \frac{2 \cdot - 3}{3}$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Simplify the expression.

Multiply $2$ by $- 3$ .

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

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Divide $- 6$ by $3$ .

$x = 2$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Multiply $- 1$ by $- 2$ .

$x = 2$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 2$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 2$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

$x = 2$

$z = 1$

$y = \frac{7}{3} + \frac{2 z}{3}$

Replace all occurrences of $z$ in $y = \frac{7}{3} + \frac{2 z}{3}$ with $1$ .

$y = \frac{7}{3} + \frac{2 (1)}{3}$

$x = 2$

$z = 1$

Simplify the right side.

Simplify $\frac{7}{3} + \frac{2 (1)}{3}$ .

Combine the numerators over the common denominator.

$y = \frac{7 + 2 (1)}{3}$

$x = 2$

$z = 1$

Simplify the expression.

Multiply $2$ by $1$ .

$y = \frac{7 + 2}{3}$

$x = 2$

$z = 1$

Add $7$ and $2$ .

$y = \frac{9}{3}$

$x = 2$

$z = 1$

Divide $9$ by $3$ .

$y = 3$

$x = 2$

$z = 1$

$y = 3$

$x = 2$

$z = 1$

$y = 3$

$x = 2$

$z = 1$

$y = 3$

$x = 2$

$z = 1$

$y = 3$

$x = 2$

$z = 1$

Step 7

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

$(2, 3, 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(2, 3, 1)$

Equation Form:

$x = 2, y = 3, z = 1$

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

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