Solve the System of Equations -x+y+3z=3 x+2y-z=0 3x+2y-5z=-2

$- x + y + 3 z = 3$ $x + 2 y - z = 0$ $3 x + 2 y - 5 z = - 2$

Step 1

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

Add $x$ to both sides of the equation.

$y + 3 z = 3 + x$

$x + 2 y - z = 0$

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

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

$y = 3 + x - 3 z$

$x + 2 y - z = 0$

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

$y = 3 + x - 3 z$

$x + 2 y - z = 0$

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

Step 2

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

Replace all occurrences of $y$ in $x + 2 y - z = 0$ with $3 + x - 3 z$ .

$x + 2 (3 + x - 3 z) - z = 0$

$y = 3 + x - 3 z$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$x + 2 \cdot 3 + 2 x + 2 (- 3 z) - z = 0$

$y = 3 + x - 3 z$

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

Simplify.

Multiply $2$ by $3$ .

$x + 6 + 2 x + 2 (- 3 z) - z = 0$

$y = 3 + x - 3 z$

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

Multiply $- 3$ by $2$ .

$x + 6 + 2 x - 6 z - z = 0$

$y = 3 + x - 3 z$

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

$x + 6 + 2 x - 6 z - z = 0$

$y = 3 + x - 3 z$

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

$x + 6 + 2 x - 6 z - z = 0$

$y = 3 + x - 3 z$

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

Simplify by adding terms.

Add $x$ and $2 x$ .

$3 x + 6 - 6 z - z = 0$

$y = 3 + x - 3 z$

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

Subtract $z$ from $- 6 z$ .

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

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

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

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

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

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

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

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

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

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

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Simplify.

Multiply $2$ by $3$ .

$3 x + 6 + 2 x + 2 (- 3 z) - 5 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Multiply $- 3$ by $2$ .

$3 x + 6 + 2 x - 6 z - 5 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$3 x + 6 + 2 x - 6 z - 5 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$3 x + 6 + 2 x - 6 z - 5 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Simplify by adding terms.

Add $3 x$ and $2 x$ .

$5 x + 6 - 6 z - 5 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Subtract $5 z$ from $- 6 z$ .

$5 x + 6 - 11 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$5 x + 6 - 11 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$5 x + 6 - 11 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$5 x + 6 - 11 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$5 x + 6 - 11 z = - 2$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Step 3

Solve for $x$ in $5 x + 6 - 11 z = - 2$ .

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

Subtract $6$ from both sides of the equation.

$5 x - 11 z = - 2 - 6$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Add $11 z$ to both sides of the equation.

$5 x = - 2 - 6 + 11 z$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Subtract $6$ from $- 2$ .

$5 x = - 8 + 11 z$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$5 x = - 8 + 11 z$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Divide each term in $5 x = - 8 + 11 z$ by $5$ and simplify.

Divide each term in $5 x = - 8 + 11 z$ by $5$ .

$\frac{5 x}{5} = \frac{- 8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Divide $x$ by $1$ .

$x = \frac{- 8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$x = \frac{- 8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$x = \frac{- 8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$3 x + 6 - 7 z = 0$

$y = 3 + x - 3 z$

Step 4

Replace all occurrences of $x$ with $- \frac{8}{5} + \frac{11 z}{5}$ in each equation.

Replace all occurrences of $x$ in $3 x + 6 - 7 z = 0$ with $- \frac{8}{5} + \frac{11 z}{5}$ .

$3 (- \frac{8}{5} + \frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Simplify the left side.

Simplify $3 (- \frac{8}{5} + \frac{11 z}{5}) + 6 - 7 z$ .

Simplify each term.

Apply the distributive property.

$3 (- \frac{8}{5}) + 3 (\frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Multiply $3 (- \frac{8}{5})$ .

Multiply $- 1$ by $3$ .

$- 3 (\frac{8}{5}) + 3 (\frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Combine $- 3$ and $\frac{8}{5}$ .

$\frac{- 3 \cdot 8}{5} + 3 (\frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Multiply $- 3$ by $8$ .

$\frac{- 24}{5} + 3 (\frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$\frac{- 24}{5} + 3 (\frac{11 z}{5}) + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Multiply $3 \frac{11 z}{5}$ .

Combine $3$ and $\frac{11 z}{5}$ .

$\frac{- 24}{5} + \frac{3 (11 z)}{5} + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Multiply $11$ by $3$ .

$\frac{- 24}{5} + \frac{33 z}{5} + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$\frac{- 24}{5} + \frac{33 z}{5} + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Move the negative in front of the fraction.

$- \frac{24}{5} + \frac{33 z}{5} + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$- \frac{24}{5} + \frac{33 z}{5} + 6 - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{33 z}{5} - \frac{24}{5} + 6 \cdot \frac{5}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Combine $6$ and $\frac{5}{5}$ .

$\frac{33 z}{5} - \frac{24}{5} + \frac{6 \cdot 5}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Combine the numerators over the common denominator.

$\frac{33 z}{5} + \frac{- 24 + 6 \cdot 5}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Simplify the numerator.

Multiply $6$ by $5$ .

$\frac{33 z}{5} + \frac{- 24 + 30}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Add $- 24$ and $30$ .

$\frac{33 z}{5} + \frac{6}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$\frac{33 z}{5} + \frac{6}{5} - 7 z = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

To write $- 7 z$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{33 z}{5} - 7 z \cdot \frac{5}{5} + \frac{6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

$\frac{33 z}{5} + \frac{- 7 z \cdot 5}{5} + \frac{6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Combine the numerators over the common denominator.

$\frac{33 z - 7 z \cdot 5}{5} + \frac{6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Combine the numerators over the common denominator.

$\frac{33 z - 7 z \cdot 5 + 6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Multiply $5$ by $- 7$ .

$\frac{33 z - 35 z + 6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Subtract $35 z$ from $33 z$ .

$\frac{- 2 z + 6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

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

$\frac{2 (- z) + 6}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Factor $2$ out of $6$ .

$\frac{2 (- z) + 2 (3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

$\frac{2 (- z + 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$\frac{2 (- z + 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

$\frac{2 (- (z) + 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

$\frac{2 (- (z) - 1 \cdot - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

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

$\frac{2 (- (z - 3))}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Simplify the expression.

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

$\frac{2 (- 1 (z - 3))}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Move the negative in front of the fraction.

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 + x - 3 z$

Replace all occurrences of $x$ in $y = 3 + x - 3 z$ with $- \frac{8}{5} + \frac{11 z}{5}$ .

$y = 3 - \frac{8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify $y = 3 - \frac{8}{5} + \frac{11 z}{5} - 3 z$ .

Simplify the left side.

Remove parentheses.

$y = 3 - \frac{8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = 3 - \frac{8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify the right side.

Simplify $3 - \frac{8}{5} + \frac{11 z}{5} - 3 z$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 3 \cdot \frac{5}{5} - \frac{8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

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

$y = \frac{3 \cdot 5}{5} - \frac{8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Combine the numerators over the common denominator.

$y = \frac{3 \cdot 5 - 8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$y = \frac{15 - 8}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Subtract $8$ from $15$ .

$y = \frac{7}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{7}{5} + \frac{11 z}{5} - 3 z$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

To write $- 3 z$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{7}{5} + \frac{11 z}{5} - 3 z \cdot \frac{5}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

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

$y = \frac{7}{5} + \frac{11 z}{5} + \frac{- 3 z \cdot 5}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Combine the numerators over the common denominator.

$y = \frac{7}{5} + \frac{11 z - 3 z \cdot 5}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Combine the numerators over the common denominator.

$y = \frac{7 + 11 z - 3 z \cdot 5}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Multiply $5$ by $- 3$ .

$y = \frac{7 + 11 z - 15 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Subtract $15 z$ from $11 z$ .

$y = \frac{7 - 4 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{7 - 4 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{7 - 4 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{7 - 4 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{7 - 4 z}{5}$

$- \frac{2 (z - 3)}{5} = 0$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Step 5

Solve for $z$ in $- \frac{2 (z - 3)}{5} = 0$ .

Set the numerator equal to zero.

$2 (z - 3) = 0$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Solve the equation for $z$ .

Divide each term in $2 (z - 3) = 0$ by $2$ and simplify.

Divide each term in $2 (z - 3) = 0$ by $2$ .

$\frac{2 (z - 3)}{2} = \frac{0}{2}$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (z - 3)}{2} = \frac{0}{2}$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Divide $z - 3$ by $1$ .

$z - 3 = \frac{0}{2}$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z - 3 = \frac{0}{2}$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z - 3 = \frac{0}{2}$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify the right side.

Divide $0$ by $2$ .

$z - 3 = 0$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z - 3 = 0$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z - 3 = 0$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Add $3$ to both sides of the equation.

$z = 3$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z = 3$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$z = 3$

$y = \frac{7 - 4 z}{5}$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Step 6

Replace all occurrences of $z$ with $3$ in each equation.

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

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

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Simplify the right side.

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

Simplify the numerator.

Multiply $- 4$ by $3$ .

$y = \frac{7 - 12}{5}$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Subtract $12$ from $7$ .

$y = \frac{- 5}{5}$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = \frac{- 5}{5}$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Divide $- 5$ by $5$ .

$y = - 1$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = - 1$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

$y = - 1$

$z = 3$

$x = - \frac{8}{5} + \frac{11 z}{5}$

Replace all occurrences of $z$ in $x = - \frac{8}{5} + \frac{11 z}{5}$ with $3$ .

$x = - \frac{8}{5} + \frac{11 (3)}{5}$

$y = - 1$

$z = 3$

Simplify the right side.

Simplify $- \frac{8}{5} + \frac{11 (3)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 8 + 11 (3)}{5}$

$y = - 1$

$z = 3$

Simplify the expression.

Multiply $11$ by $3$ .

$x = \frac{- 8 + 33}{5}$

$y = - 1$

$z = 3$

Add $- 8$ and $33$ .

$x = \frac{25}{5}$

$y = - 1$

$z = 3$

Divide $25$ by $5$ .

$x = 5$

$y = - 1$

$z = 3$

$x = 5$

$y = - 1$

$z = 3$

$x = 5$

$y = - 1$

$z = 3$

$x = 5$

$y = - 1$

$z = 3$

$x = 5$

$y = - 1$

$z = 3$

Step 7

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

$(5, - 1, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(5, - 1, 3)$

Equation Form:

$x = 5, y = - 1, z = 3$

Solve the System of Equations -x+y+3z=3 x+2y-z=0 3x+2y-5z=-2

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