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

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

Step 1

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

Subtract $y$ from both sides of the equation.

$x - z = - 1 - y$

$- 2 x + y + z = 7$

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

Add $z$ to both sides of the equation.

$x = - 1 - y + z$

$- 2 x + y + z = 7$

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

$x = - 1 - y + z$

$- 2 x + y + z = 7$

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

Step 2

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

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

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

$x = - 1 - y + z$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = - 1 - y + z$

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

Simplify.

Multiply $- 2$ by $- 1$ .

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

$x = - 1 - y + z$

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

Multiply $- 1$ by $- 2$ .

$2 + 2 y - 2 z + y + z = 7$

$x = - 1 - y + z$

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

$2 + 2 y - 2 z + y + z = 7$

$x = - 1 - y + z$

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

$2 + 2 y - 2 z + y + z = 7$

$x = - 1 - y + z$

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

Simplify by adding terms.

Add $2 y$ and $y$ .

$2 + 3 y - 2 z + z = 7$

$x = - 1 - y + z$

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

Add $- 2 z$ and $z$ .

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Simplify.

Multiply $2$ by $- 1$ .

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Multiply $- 1$ by $2$ .

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Simplify by adding terms.

Subtract $2 y$ from $- 2 y$ .

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Add $2 z$ and $4 z$ .

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Step 3

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

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

Add $2$ to both sides of the equation.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Subtract $6 z$ from both sides of the equation.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Add $- 4$ and $2$ .

$- 4 y = - 2 - 6 z$

$2 + 3 y - z = 7$

$x = - 1 - y + z$

$- 4 y = - 2 - 6 z$

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Divide $y$ by $1$ .

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Simplify the right side.

Simplify each term.

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

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Cancel the common factors.

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Cancel the common factor.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Rewrite the expression.

$y = \frac{1}{2} + \frac{- 6 z}{- 4}$

$2 + 3 y - z = 7$

$x = - 1 - y + z$

$y = \frac{1}{2} + \frac{- 6 z}{- 4}$

$2 + 3 y - z = 7$

$x = - 1 - y + z$

$y = \frac{1}{2} + \frac{- 6 z}{- 4}$

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Cancel the common factors.

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

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Cancel the common factor.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Rewrite the expression.

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

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

$2 + 3 y - z = 7$

$x = - 1 - y + z$

Step 4

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

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

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

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

$x = - 1 - y + z$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

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

$x = - 1 - y + z$

Combine $3$ and $\frac{1}{2}$ .

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

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

$x = - 1 - y + z$

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

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

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

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

$x = - 1 - y + z$

Multiply $3$ by $3$ .

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

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

$x = - 1 - y + z$

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

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

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

$x = - 1 - y + z$

Combine the numerators over the common denominator.

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

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

$x = - 1 - y + z$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 + 3}{2} + \frac{9 z}{2} - z = 7$

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

$x = - 1 - y + z$

Add $4$ and $3$ .

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

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

$x = - 1 - y + z$

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

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

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

$x = - 1 - y + z$

Combine the numerators over the common denominator.

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

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

$x = - 1 - y + z$

Combine the numerators over the common denominator.

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

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

$x = - 1 - y + z$

Multiply $2$ by $- 1$ .

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

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

$x = - 1 - y + z$

Subtract $2 z$ from $9 z$ .

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

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

$x = - 1 - y + z$

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

Factor $7$ out of $7$ .

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

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

$x = - 1 - y + z$

Factor $7$ out of $7 \cdot 1 + 7 z$ .

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

$x = - 1 - y + z$

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

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

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

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

Simplify the right side.

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

Apply the distributive property.

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

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

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine $- 1$ and $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

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

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

Simplify the numerator.

Multiply $- 1$ by $2$ .

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

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

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

Subtract $1$ from $- 2$ .

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

Simplify terms.

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

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

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

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

Combine the numerators over the common denominator.

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

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

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

Combine the numerators over the common denominator.

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

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

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

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

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

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

Move $2$ to the left of $z$ .

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

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

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

Simplify terms.

Add $- 3 z$ and $2 z$ .

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

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

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

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

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

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

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

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

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

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

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

Factor $- 1$ out of $- 1 (3) - (z)$ .

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 5

Solve for $z$ in $\frac{7 (1 + z)}{2} = 7$ .

Multiply both sides of the equation by $\frac{2}{7}$ .

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

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

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

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Rewrite the expression.

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

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

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

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

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

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

Cancel the common factor of $7$ .

Cancel the common factor.

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

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

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Simplify the right side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

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

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

Rewrite the expression.

$1 + z = 2$

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

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

$1 + z = 2$

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

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

$1 + z = 2$

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

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

$1 + z = 2$

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

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

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

Subtract $1$ from both sides of the equation.

$z = 2 - 1$

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

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

Subtract $1$ from $2$ .

$z = 1$

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

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

$z = 1$

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

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

$z = 1$

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

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

Step 6

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

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

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

$z = 1$

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

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

Simplify the left side.

Remove parentheses.

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

$z = 1$

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

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

$z = 1$

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

Simplify the right side.

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

Add $3$ and $1$ .

$x = - \frac{4}{2}$

$z = 1$

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

Divide $4$ by $2$ .

$x = - 1 \cdot 2$

$z = 1$

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

Multiply $- 1$ by $2$ .

$x = - 2$

$z = 1$

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

$x = - 2$

$z = 1$

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

$x = - 2$

$z = 1$

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

$x = - 2$

$z = 1$

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

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

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

$x = - 2$

$z = 1$

Simplify the right side.

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

Combine the numerators over the common denominator.

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

$x = - 2$

$z = 1$

Simplify the expression.

Multiply $3$ by $1$ .

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

$x = - 2$

$z = 1$

Add $1$ and $3$ .

$y = \frac{4}{2}$

$x = - 2$

$z = 1$

Divide $4$ by $2$ .

$y = 2$

$x = - 2$

$z = 1$

$y = 2$

$x = - 2$

$z = 1$

$y = 2$

$x = - 2$

$z = 1$

$y = 2$

$x = - 2$

$z = 1$

$y = 2$

$x = - 2$

$z = 1$

Step 7

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

$(- 2, 2, 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 2, 2, 1)$

Equation Form:

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

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

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