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

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

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

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

$y + z = - 3 - 2 x$

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

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

Subtract $z$ from both sides of the equation.

$y = - 3 - 2 x - z$

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

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

$y = - 3 - 2 x - z$

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

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

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

Replace all occurrences of $y$ in $3 x - 5 y + 3 z = - 4$ with $- 3 - 2 x - z$ .

$3 x - 5 (- 3 - 2 x - z) + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Simplify the left side.

Simplify $3 x - 5 (- 3 - 2 x - z) + 3 z$ .

Simplify each term.

Apply the distributive property.

$3 x - 5 \cdot - 3 - 5 (- 2 x) - 5 (- z) + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Simplify.

Multiply $- 5$ by $- 3$ .

$3 x + 15 - 5 (- 2 x) - 5 (- z) + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Multiply $- 2$ by $- 5$ .

$3 x + 15 + 10 x - 5 (- z) + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Multiply $- 1$ by $- 5$ .

$3 x + 15 + 10 x + 5 z + 3 z = - 4$

$y = - 3 - 2 x - z$

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

$3 x + 15 + 10 x + 5 z + 3 z = - 4$

$y = - 3 - 2 x - z$

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

$3 x + 15 + 10 x + 5 z + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Simplify by adding terms.

Add $3 x$ and $10 x$ .

$13 x + 15 + 5 z + 3 z = - 4$

$y = - 3 - 2 x - z$

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

Add $5 z$ and $3 z$ .

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

Replace all occurrences of $y$ in $5 x - y + 2 z = - 2$ with $- 3 - 2 x - z$ .

$5 x - (- 3 - 2 x - z) + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Simplify the left side.

Simplify $5 x - (- 3 - 2 x - z) + 2 z$ .

Simplify each term.

Apply the distributive property.

$5 x + 3 - (- 2 x) + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Simplify.

Multiply $- 1$ by $- 3$ .

$5 x + 3 - (- 2 x) + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Multiply $- 2$ by $- 1$ .

$5 x + 3 + 2 x + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Multiply $- - z$ .

Multiply $- 1$ by $- 1$ .

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Multiply $z$ by $1$ .

$5 x + 3 + 2 x + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$5 x + 3 + 2 x + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$5 x + 3 + 2 x + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$5 x + 3 + 2 x + z + 2 z = - 2$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Simplify by adding terms.

Add $5 x$ and $2 x$ .

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Add $z$ and $2 z$ .

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Solve for $x$ in $7 x + 3 + 3 z = - 2$ .

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

Subtract $3$ from both sides of the equation.

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

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

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

$7 x = - 2 - 3 - 3 z$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Subtract $3$ from $- 2$ .

$7 x = - 5 - 3 z$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$7 x = - 5 - 3 z$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Divide each term in $7 x = - 5 - 3 z$ by $7$ and simplify.

Divide each term in $7 x = - 5 - 3 z$ by $7$ .

$\frac{7 x}{7} = \frac{- 5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Divide $x$ by $1$ .

$x = \frac{- 5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = \frac{- 5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = \frac{- 5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{5}{7} + \frac{- 3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Move the negative in front of the fraction.

$x = - \frac{5}{7} - \frac{3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$13 x + 15 + 8 z = - 4$

$y = - 3 - 2 x - z$

Replace all occurrences of $x$ with $- \frac{5}{7} - \frac{3 z}{7}$ in each equation.

Replace all occurrences of $x$ in $13 x + 15 + 8 z = - 4$ with $- \frac{5}{7} - \frac{3 z}{7}$ .

$13 (- \frac{5}{7} - \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Simplify the left side.

Simplify $13 (- \frac{5}{7} - \frac{3 z}{7}) + 15 + 8 z$ .

Simplify each term.

Apply the distributive property.

$13 (- \frac{5}{7}) + 13 (- \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Multiply $13 (- \frac{5}{7})$ .

Multiply $- 1$ by $13$ .

$- 13 (\frac{5}{7}) + 13 (- \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine $- 13$ and $\frac{5}{7}$ .

$\frac{- 13 \cdot 5}{7} + 13 (- \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Multiply $- 13$ by $5$ .

$\frac{- 65}{7} + 13 (- \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$\frac{- 65}{7} + 13 (- \frac{3 z}{7}) + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Multiply $13 (- \frac{3 z}{7})$ .

Multiply $- 1$ by $13$ .

$\frac{- 65}{7} - 13 \frac{3 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine $- 13$ and $\frac{3 z}{7}$ .

$\frac{- 65}{7} + \frac{- 13 (3 z)}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Multiply $3$ by $- 13$ .

$\frac{- 65}{7} + \frac{- 39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$\frac{- 65}{7} + \frac{- 39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{65}{7} + \frac{- 39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Move the negative in front of the fraction.

$- \frac{65}{7} - \frac{39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$- \frac{65}{7} - \frac{39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$- \frac{65}{7} - \frac{39 z}{7} + 15 + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

To write $15$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{39 z}{7} - \frac{65}{7} + 15 \cdot \frac{7}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine $15$ and $\frac{7}{7}$ .

$- \frac{39 z}{7} - \frac{65}{7} + \frac{15 \cdot 7}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine the numerators over the common denominator.

$- \frac{39 z}{7} + \frac{- 65 + 15 \cdot 7}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Simplify the numerator.

Multiply $15$ by $7$ .

$- \frac{39 z}{7} + \frac{- 65 + 105}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Add $- 65$ and $105$ .

$- \frac{39 z}{7} + \frac{40}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$- \frac{39 z}{7} + \frac{40}{7} + 8 z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

To write $8 z$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{39 z}{7} + 8 z \cdot \frac{7}{7} + \frac{40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine $8 z$ and $\frac{7}{7}$ .

$- \frac{39 z}{7} + \frac{8 z \cdot 7}{7} + \frac{40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine the numerators over the common denominator.

$\frac{- 39 z + 8 z \cdot 7}{7} + \frac{40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Combine the numerators over the common denominator.

$\frac{- 39 z + 8 z \cdot 7 + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Multiply $7$ by $8$ .

$\frac{- 39 z + 56 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

Add $- 39 z$ and $56 z$ .

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 - 2 x - z$

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

$y = - 3 - 2 (- \frac{5}{7} - \frac{3 z}{7}) - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the right side.

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

Simplify each term.

Apply the distributive property.

$y = - 3 - 2 (- \frac{5}{7}) - 2 (- \frac{3 z}{7}) - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Multiply $- 2 (- \frac{5}{7})$ .

Multiply $- 1$ by $- 2$ .

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

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Combine $2$ and $\frac{5}{7}$ .

$y = - 3 + \frac{2 \cdot 5}{7} - 2 (- \frac{3 z}{7}) - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Multiply $2$ by $5$ .

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

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

Multiply $- 1$ by $- 2$ .

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

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

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

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Multiply $3$ by $2$ .

$y = - 3 + \frac{10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 + \frac{10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 3 + \frac{10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - 3 \cdot \frac{7}{7} + \frac{10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

$y = \frac{- 3 \cdot 7}{7} + \frac{10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 7 + 10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the numerator.

Multiply $- 3$ by $7$ .

$y = \frac{- 21 + 10}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Add $- 21$ and $10$ .

$y = \frac{- 11}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = \frac{- 11}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Move the negative in front of the fraction.

$y = - \frac{11}{7} + \frac{6 z}{7} - z$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

To write $- z$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{11}{7} + \frac{6 z}{7} - z \cdot \frac{7}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Combine $- z$ and $\frac{7}{7}$ .

$y = - \frac{11}{7} + \frac{6 z}{7} + \frac{- z \cdot 7}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Combine the numerators over the common denominator.

$y = - \frac{11}{7} + \frac{6 z - z \cdot 7}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Combine the numerators over the common denominator.

$y = \frac{- 11 + 6 z - z \cdot 7}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Multiply $7$ by $- 1$ .

$y = \frac{- 11 + 6 z - 7 z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Subtract $7 z$ from $6 z$ .

$y = \frac{- 11 - z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

$y = \frac{- 1 \cdot 11 - z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

$y = \frac{- 1 \cdot 11 - (z)}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

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

$y = \frac{- 1 (11 + z)}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Move the negative in front of the fraction.

$y = - \frac{11 + z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - \frac{11 + z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - \frac{11 + z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - \frac{11 + z}{7}$

$\frac{17 z + 40}{7} = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Solve for $z$ in $\frac{17 z + 40}{7} = - 4$ .

Multiply both sides by $7$ .

$\frac{17 z + 40}{7} \cdot 7 = - 4 \cdot 7$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{17 z + 40}{7} \cdot 7 = - 4 \cdot 7$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Rewrite the expression.

$17 z + 40 = - 4 \cdot 7$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$17 z + 40 = - 4 \cdot 7$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$17 z + 40 = - 4 \cdot 7$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the right side.

Multiply $- 4$ by $7$ .

$17 z + 40 = - 28$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$17 z + 40 = - 28$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$17 z + 40 = - 28$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Solve for $z$ .

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

Subtract $40$ from both sides of the equation.

$17 z = - 28 - 40$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Subtract $40$ from $- 28$ .

$17 z = - 68$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$17 z = - 68$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Divide each term in $17 z = - 68$ by $17$ and simplify.

Divide each term in $17 z = - 68$ by $17$ .

$\frac{17 z}{17} = \frac{- 68}{17}$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 z}{17} = \frac{- 68}{17}$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Divide $z$ by $1$ .

$z = \frac{- 68}{17}$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = \frac{- 68}{17}$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = \frac{- 68}{17}$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the right side.

Divide $- 68$ by $17$ .

$z = - 4$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = - 4$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = - 4$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = - 4$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$z = - 4$

$y = - \frac{11 + z}{7}$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Replace all occurrences of $z$ with $- 4$ in each equation.

Replace all occurrences of $z$ in $y = - \frac{11 + z}{7}$ with $- 4$ .

$y = - \frac{11 - 4}{7}$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify $y = - \frac{11 - 4}{7}$ .

Simplify the left side.

Remove parentheses.

$y = - \frac{11 - 4}{7}$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - \frac{11 - 4}{7}$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Simplify the right side.

Simplify $- \frac{11 - 4}{7}$ .

Subtract $4$ from $11$ .

$y = - \frac{7}{7}$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Cancel the common factor of $7$ .

Cancel the common factor.

$y = - \frac{7}{7}$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Rewrite the expression.

$y = - 1 \cdot 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 1 \cdot 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Multiply $- 1$ by $1$ .

$y = - 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

$y = - 1$

$z = - 4$

$x = - \frac{5}{7} - \frac{3 z}{7}$

Replace all occurrences of $z$ in $x = - \frac{5}{7} - \frac{3 z}{7}$ with $- 4$ .

$x = - \frac{5}{7} - \frac{3 (- 4)}{7}$

$y = - 1$

$z = - 4$

Simplify the right side.

Simplify $- \frac{5}{7} - \frac{3 (- 4)}{7}$ .

Combine the numerators over the common denominator.

$x = \frac{- 5 - 3 \cdot - 4}{7}$

$y = - 1$

$z = - 4$

Simplify the expression.

Multiply $- 3$ by $- 4$ .

$x = \frac{- 5 + 12}{7}$

$y = - 1$

$z = - 4$

Add $- 5$ and $12$ .

$x = \frac{7}{7}$

$y = - 1$

$z = - 4$

Divide $7$ by $7$ .

$x = 1$

$y = - 1$

$z = - 4$

$x = 1$

$y = - 1$

$z = - 4$

$x = 1$

$y = - 1$

$z = - 4$

$x = 1$

$y = - 1$

$z = - 4$

$x = 1$

$y = - 1$

$z = - 4$

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

$(1, - 1, - 4)$

The result can be shown in multiple forms.

Point Form:

$(1, - 1, - 4)$

Equation Form:

$x = 1, y = - 1, z = - 4$

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

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