Solve the System of Equations -x+y+z=-1 x-2y+z=7 4x+2y-2z=-4

$- x + y + z = - 1$ $x - 2 y + z = 7$ $4 x + 2 y - 2 z = - 4$

Step 1

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

Add $x$ to both sides of the equation.

$y + z = - 1 + x$

$x - 2 y + z = 7$

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

Subtract $z$ from both sides of the equation.

$y = - 1 + x - z$

$x - 2 y + z = 7$

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

$y = - 1 + x - z$

$x - 2 y + z = 7$

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

Step 2

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

Replace all occurrences of $y$ in $x - 2 y + z = 7$ with $- 1 + x - z$ .

$x - 2 (- 1 + x - z) + z = 7$

$y = - 1 + x - z$

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

Simplify the left side.

Simplify $x - 2 (- 1 + x - z) + z$ .

Simplify each term.

Apply the distributive property.

$x - 2 \cdot - 1 - 2 x - 2 (- z) + z = 7$

$y = - 1 + x - z$

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

Simplify.

Multiply $- 2$ by $- 1$ .

$x + 2 - 2 x - 2 (- z) + z = 7$

$y = - 1 + x - z$

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

Multiply $- 1$ by $- 2$ .

$x + 2 - 2 x + 2 z + z = 7$

$y = - 1 + x - z$

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

$x + 2 - 2 x + 2 z + z = 7$

$y = - 1 + x - z$

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

$x + 2 - 2 x + 2 z + z = 7$

$y = - 1 + x - z$

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

Simplify by adding terms.

Subtract $2 x$ from $x$ .

$- x + 2 + 2 z + z = 7$

$y = - 1 + x - z$

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

Add $2 z$ and $z$ .

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

Replace all occurrences of $y$ in $4 x + 2 y - 2 z = - 4$ with $- 1 + x - z$ .

$4 x + 2 (- 1 + x - z) - 2 z = - 4$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Simplify the left side.

Simplify $4 x + 2 (- 1 + x - z) - 2 z$ .

Simplify each term.

Apply the distributive property.

$4 x + 2 \cdot - 1 + 2 x + 2 (- z) - 2 z = - 4$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Simplify.

Multiply $2$ by $- 1$ .

$4 x - 2 + 2 x + 2 (- z) - 2 z = - 4$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Multiply $- 1$ by $2$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Simplify by adding terms.

Add $4 x$ and $2 x$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Subtract $2 z$ from $- 2 z$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Step 3

Solve for $x$ in $6 x - 2 - 4 z = - 4$ .

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

Add $2$ to both sides of the equation.

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Add $- 4$ and $2$ .

$6 x = - 2 + 4 z$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

$6 x = - 2 + 4 z$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

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

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Divide $x$ by $1$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$x = \frac{2 (- 1)}{6} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 1}{2 \cdot 3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Cancel the common factor.

$x = \frac{2 \cdot - 1}{2 \cdot 3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Rewrite the expression.

$x = \frac{- 1}{3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

$x = \frac{- 1}{3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

$x = \frac{- 1}{3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Move the negative in front of the fraction.

$x = - \frac{1}{3} + \frac{4 z}{6}$

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

Factor $2$ out of $4 z$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Cancel the common factors.

Factor $2$ out of $6$ .

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Cancel the common factor.

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Rewrite the expression.

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

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

$- x + 2 + 3 z = 7$

$y = - 1 + x - z$

Step 4

Replace all occurrences of $x$ with $- \frac{1}{3} + \frac{2 z}{3}$ in each equation.

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

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

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

$y = - 1 + x - z$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

$y = - 1 + x - z$

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

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

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

$y = - 1 + x - z$

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

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

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

$y = - 1 + x - z$

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

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

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

$y = - 1 + x - z$

Combine the numerators over the common denominator.

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

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

$y = - 1 + x - z$

Simplify the numerator.

Multiply $2$ by $3$ .

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

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

$y = - 1 + x - z$

Add $1$ and $6$ .

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

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

$y = - 1 + x - z$

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

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

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

$y = - 1 + x - z$

Combine the numerators over the common denominator.

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

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

$y = - 1 + x - z$

Combine the numerators over the common denominator.

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

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

$y = - 1 + x - z$

Multiply $3$ by $3$ .

$\frac{- 2 z + 9 z + 7}{3} = 7$

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

$y = - 1 + x - z$

Add $- 2 z$ and $9 z$ .

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

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

$y = - 1 + x - z$

Factor $7$ out of $7 z + 7$ .

Factor $7$ out of $7 z$ .

$\frac{7 (z) + 7}{3} = 7$

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

$y = - 1 + x - z$

Factor $7$ out of $7$ .

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

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

$y = - 1 + x - z$

Factor $7$ out of $7 (z) + 7 (1)$ .

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

$y = - 1 + x - z$

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

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

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

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

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

Simplify the left side.

Remove parentheses.

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

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

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

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

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

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

Simplify the right side.

Simplify $- 1 - \frac{1}{3} + \frac{2 z}{3} - z$ .

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

Combine $- 1$ and $\frac{3}{3}$ .

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

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

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

Combine the numerators over the common denominator.

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

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

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

Simplify the numerator.

Multiply $- 1$ by $3$ .

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

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

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

Subtract $1$ from $- 3$ .

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

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

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

Combine the numerators over the common denominator.

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

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

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

Multiply $3$ by $- 1$ .

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

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

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

Subtract $3 z$ from $2 z$ .

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

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

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

Rewrite $- 4$ as $- 1 (4)$ .

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

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

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

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

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

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 5

Solve for $z$ in $\frac{7 (z + 1)}{3} = 7$ .

Multiply both sides of the equation by $\frac{3}{7}$ .

$\frac{3}{7} \cdot \frac{7 (z + 1)}{3} = \frac{3}{7} \cdot 7$

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

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{7} \cdot \frac{7 (z + 1)}{3} = \frac{3}{7} \cdot 7$

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

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

Rewrite the expression.

$\frac{1}{7} \cdot (7 (z + 1)) = \frac{3}{7} \cdot 7$

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

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

$\frac{1}{7} \cdot (7 (z + 1)) = \frac{3}{7} \cdot 7$

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

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

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{1}{7} \cdot (7 (z + 1)) = \frac{3}{7} \cdot 7$

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

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Simplify the right side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

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

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

Rewrite the expression.

$z + 1 = 3$

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

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

$z + 1 = 3$

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

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

$z + 1 = 3$

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

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

$z + 1 = 3$

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

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

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

Subtract $1$ from both sides of the equation.

$z = 3 - 1$

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

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

Subtract $1$ from $3$ .

$z = 2$

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

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

$z = 2$

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

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

$z = 2$

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

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

Step 6

Replace all occurrences of $z$ with $2$ in each equation.

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

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

$z = 2$

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

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

Simplify the left side.

Remove parentheses.

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

$z = 2$

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

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

$z = 2$

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

Simplify the right side.

Simplify $- \frac{4 + 2}{3}$ .

Add $4$ and $2$ .

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

$z = 2$

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

Divide $6$ by $3$ .

$y = - 1 \cdot 2$

$z = 2$

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

Multiply $- 1$ by $2$ .

$y = - 2$

$z = 2$

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

$y = - 2$

$z = 2$

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

$y = - 2$

$z = 2$

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

$y = - 2$

$z = 2$

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

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

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

$y = - 2$

$z = 2$

Simplify the right side.

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

Combine the numerators over the common denominator.

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

$y = - 2$

$z = 2$

Simplify the expression.

Multiply $2$ by $2$ .

$x = \frac{- 1 + 4}{3}$

$y = - 2$

$z = 2$

Add $- 1$ and $4$ .

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

$y = - 2$

$z = 2$

Divide $3$ by $3$ .

$x = 1$

$y = - 2$

$z = 2$

$x = 1$

$y = - 2$

$z = 2$

$x = 1$

$y = - 2$

$z = 2$

$x = 1$

$y = - 2$

$z = 2$

$x = 1$

$y = - 2$

$z = 2$

Step 7

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

$(1, - 2, 2)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, - 2, 2)$

Equation Form:

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

Solve the System of Equations -x+y+z=-1 x-2y+z=7 4x+2y-2z=-4

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