Solve the System of Equations -3x+4y-z=-10 x+6y-z=-6 -2x-5y+z=2

$- 3 x + 4 y - z = - 10$ $x + 6 y - z = - 6$ $- 2 x - 5 y + z = 2$

Step 1

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

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

$x - z = - 6 - 6 y$

$- 3 x + 4 y - z = - 10$

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

Add $z$ to both sides of the equation.

$x = - 6 - 6 y + z$

$- 3 x + 4 y - z = - 10$

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

$x = - 6 - 6 y + z$

$- 3 x + 4 y - z = - 10$

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

Step 2

Replace all occurrences of $x$ with $- 6 - 6 y + z$ in each equation.

Replace all occurrences of $x$ in $- 3 x + 4 y - z = - 10$ with $- 6 - 6 y + z$ .

$- 3 (- 6 - 6 y + z) + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

Simplify the left side.

Simplify $- 3 (- 6 - 6 y + z) + 4 y - z$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 6 - 3 (- 6 y) - 3 z + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

Simplify.

Multiply $- 3$ by $- 6$ .

$18 - 3 (- 6 y) - 3 z + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

Multiply $- 6$ by $- 3$ .

$18 + 18 y - 3 z + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 18 y - 3 z + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 18 y - 3 z + 4 y - z = - 10$

$x = - 6 - 6 y + z$

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

Simplify by adding terms.

Add $18 y$ and $4 y$ .

$18 + 22 y - 3 z - z = - 10$

$x = - 6 - 6 y + z$

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

Subtract $z$ from $- 3 z$ .

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

Replace all occurrences of $x$ in $- 2 x - 5 y + z = 2$ with $- 6 - 6 y + z$ .

$- 2 (- 6 - 6 y + z) - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Simplify the left side.

Simplify $- 2 (- 6 - 6 y + z) - 5 y + z$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot - 6 - 2 (- 6 y) - 2 z - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Simplify.

Multiply $- 2$ by $- 6$ .

$12 - 2 (- 6 y) - 2 z - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Multiply $- 6$ by $- 2$ .

$12 + 12 y - 2 z - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 12 y - 2 z - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 12 y - 2 z - 5 y + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Simplify by adding terms.

Subtract $5 y$ from $12 y$ .

$12 + 7 y - 2 z + z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Add $- 2 z$ and $z$ .

$12 + 7 y - z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 7 y - z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 7 y - z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 7 y - z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$12 + 7 y - z = 2$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Step 3

Solve for $y$ in $12 + 7 y - z = 2$ .

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

Subtract $12$ from both sides of the equation.

$7 y - z = 2 - 12$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Add $z$ to both sides of the equation.

$7 y = 2 - 12 + z$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Subtract $12$ from $2$ .

$7 y = - 10 + z$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

$7 y = - 10 + z$

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Divide each term in $7 y = - 10 + z$ by $7$ and simplify.

Divide each term in $7 y = - 10 + z$ by $7$ .

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Divide $y$ by $1$ .

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Simplify the right side.

Move the negative in front of the fraction.

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

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

$18 + 22 y - 4 z = - 10$

$x = - 6 - 6 y + z$

Step 4

Replace all occurrences of $y$ with $- \frac{10}{7} + \frac{z}{7}$ in each equation.

Replace all occurrences of $y$ in $18 + 22 y - 4 z = - 10$ with $- \frac{10}{7} + \frac{z}{7}$ .

$18 + 22 (- \frac{10}{7} + \frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Simplify the left side.

Simplify $18 + 22 (- \frac{10}{7} + \frac{z}{7}) - 4 z$ .

Simplify each term.

Apply the distributive property.

$18 + 22 (- \frac{10}{7}) + 22 (\frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Multiply $22 (- \frac{10}{7})$ .

Multiply $- 1$ by $22$ .

$18 - 22 (\frac{10}{7}) + 22 (\frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Combine $- 22$ and $\frac{10}{7}$ .

$18 + \frac{- 22 \cdot 10}{7} + 22 (\frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Multiply $- 22$ by $10$ .

$18 + \frac{- 220}{7} + 22 (\frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

$18 + \frac{- 220}{7} + 22 (\frac{z}{7}) - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Combine $22$ and $\frac{z}{7}$ .

$18 + \frac{- 220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Move the negative in front of the fraction.

$18 - \frac{220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

$18 - \frac{220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

To write $18$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$18 \cdot \frac{7}{7} - \frac{220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Combine $18$ and $\frac{7}{7}$ .

$\frac{18 \cdot 7}{7} - \frac{220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Combine the numerators over the common denominator.

$\frac{18 \cdot 7 - 220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Simplify the numerator.

Multiply $18$ by $7$ .

$\frac{126 - 220}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Subtract $220$ from $126$ .

$\frac{- 94}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

$\frac{- 94}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

Move the negative in front of the fraction.

$- \frac{94}{7} + \frac{22 z}{7} - 4 z = - 10$

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

$x = - 6 - 6 y + z$

To write $- 4 z$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{94}{7} + \frac{22 z}{7} - 4 z \cdot \frac{7}{7} = - 10$

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

$x = - 6 - 6 y + z$

Combine $- 4 z$ and $\frac{7}{7}$ .

$- \frac{94}{7} + \frac{22 z}{7} + \frac{- 4 z \cdot 7}{7} = - 10$

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

$x = - 6 - 6 y + z$

Combine the numerators over the common denominator.

$- \frac{94}{7} + \frac{22 z - 4 z \cdot 7}{7} = - 10$

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

$x = - 6 - 6 y + z$

Combine the numerators over the common denominator.

$\frac{- 94 + 22 z - 4 z \cdot 7}{7} = - 10$

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

$x = - 6 - 6 y + z$

Multiply $7$ by $- 4$ .

$\frac{- 94 + 22 z - 28 z}{7} = - 10$

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

$x = - 6 - 6 y + z$

Subtract $28 z$ from $22 z$ .

$\frac{- 94 - 6 z}{7} = - 10$

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

$x = - 6 - 6 y + z$

Factor $2$ out of $- 94 - 6 z$ .

Factor $2$ out of $- 94$ .

$\frac{2 (- 47) - 6 z}{7} = - 10$

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

$x = - 6 - 6 y + z$

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

$\frac{2 (- 47) + 2 (- 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

Factor $2$ out of $2 (- 47) + 2 (- 3 z)$ .

$\frac{2 (- 47 - 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

$\frac{2 (- 47 - 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

Rewrite $- 47$ as $- 1 (47)$ .

$\frac{2 (- 1 \cdot 47 - 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

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

$\frac{2 (- 1 \cdot 47 - (3 z))}{7} = - 10$

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

$x = - 6 - 6 y + z$

Factor $- 1$ out of $- 1 (47) - (3 z)$ .

$\frac{2 (- 1 (47 + 3 z))}{7} = - 10$

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

$x = - 6 - 6 y + z$

Move the negative in front of the fraction.

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = - 6 - 6 y + z$

Replace all occurrences of $y$ in $x = - 6 - 6 y + z$ with $- \frac{10}{7} + \frac{z}{7}$ .

$x = - 6 - 6 (- \frac{10}{7} + \frac{z}{7}) + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Simplify the right side.

Simplify $- 6 - 6 (- \frac{10}{7} + \frac{z}{7}) + z$ .

Simplify each term.

Apply the distributive property.

$x = - 6 - 6 (- \frac{10}{7}) - 6 \frac{z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Multiply $- 6 (- \frac{10}{7})$ .

Multiply $- 1$ by $- 6$ .

$x = - 6 + 6 (\frac{10}{7}) - 6 \frac{z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine $6$ and $\frac{10}{7}$ .

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

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Multiply $6$ by $10$ .

$x = - 6 + \frac{60}{7} - 6 \frac{z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = - 6 + \frac{60}{7} - 6 \frac{z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine $- 6$ and $\frac{z}{7}$ .

$x = - 6 + \frac{60}{7} + \frac{- 6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Move the negative in front of the fraction.

$x = - 6 + \frac{60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = - 6 + \frac{60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = - 6 \cdot \frac{7}{7} + \frac{60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine $- 6$ and $\frac{7}{7}$ .

$x = \frac{- 6 \cdot 7}{7} + \frac{60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine the numerators over the common denominator.

$x = \frac{- 6 \cdot 7 + 60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Simplify the numerator.

Multiply $- 6$ by $7$ .

$x = \frac{- 42 + 60}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Add $- 42$ and $60$ .

$x = \frac{18}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = \frac{18}{7} - \frac{6 z}{7} + z$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

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

$x = \frac{18}{7} - \frac{6 z}{7} + z \cdot \frac{7}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Simplify terms.

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

$x = \frac{18}{7} - \frac{6 z}{7} + \frac{z \cdot 7}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine the numerators over the common denominator.

$x = \frac{18}{7} + \frac{- 6 z + z \cdot 7}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Combine the numerators over the common denominator.

$x = \frac{18 - 6 z + z \cdot 7}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = \frac{18 - 6 z + z \cdot 7}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Move $7$ to the left of $z$ .

$x = \frac{18 - 6 z + 7 z}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Add $- 6 z$ and $7 z$ .

$x = \frac{18 + z}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = \frac{18 + z}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = \frac{18 + z}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

$x = \frac{18 + z}{7}$

$- \frac{2 (47 + 3 z)}{7} = - 10$

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

Step 5

Solve for $z$ in $- \frac{2 (47 + 3 z)}{7} = - 10$ .

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

$- \frac{7}{2} \cdot (- \frac{2 (47 + 3 z)}{7}) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{7}{2} (- \frac{2 (47 + 3 z)}{7})$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{- 7}{2} \cdot (- \frac{2 (47 + 3 z)}{7}) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Move the leading negative in $- \frac{2 (47 + 3 z)}{7}$ into the numerator.

$\frac{- 7}{2} \cdot \frac{- 2 (47 + 3 z)}{7} = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{2} \cdot \frac{- 2 (47 + 3 z)}{7} = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Cancel the common factor.

$\frac{7 \cdot - 1}{2} \cdot \frac{- 2 (47 + 3 z)}{7} = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Rewrite the expression.

$\frac{- 1}{2} \cdot (- 2 (47 + 3 z)) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

$\frac{- 1}{2} \cdot (- 2 (47 + 3 z)) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 (47 + 3 z)$ .

$\frac{- 1}{2} \cdot (2 (- (47 + 3 z))) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 (- (47 + 3 z))) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Rewrite the expression.

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (47 + 3 z) = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Multiply $47 + 3 z$ by $1$ .

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = - \frac{7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Simplify the right side.

Simplify $- \frac{7}{2} \cdot - 10$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$47 + 3 z = \frac{- 7}{2} \cdot - 10$

$x = \frac{18 + z}{7}$

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

Factor $2$ out of $- 10$ .

$47 + 3 z = \frac{- 7}{2} \cdot (2 (- 5))$

$x = \frac{18 + z}{7}$

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

Cancel the common factor.

$47 + 3 z = \frac{- 7}{2} \cdot (2 \cdot - 5)$

$x = \frac{18 + z}{7}$

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

Rewrite the expression.

$47 + 3 z = - 7 \cdot - 5$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = - 7 \cdot - 5$

$x = \frac{18 + z}{7}$

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

Multiply $- 7$ by $- 5$ .

$47 + 3 z = 35$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = 35$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = 35$

$x = \frac{18 + z}{7}$

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

$47 + 3 z = 35$

$x = \frac{18 + z}{7}$

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

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

Subtract $47$ from both sides of the equation.

$3 z = 35 - 47$

$x = \frac{18 + z}{7}$

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

Subtract $47$ from $35$ .

$3 z = - 12$

$x = \frac{18 + z}{7}$

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

$3 z = - 12$

$x = \frac{18 + z}{7}$

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

Divide each term in $3 z = - 12$ by $3$ and simplify.

Divide each term in $3 z = - 12$ by $3$ .

$\frac{3 z}{3} = \frac{- 12}{3}$

$x = \frac{18 + z}{7}$

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 z}{3} = \frac{- 12}{3}$

$x = \frac{18 + z}{7}$

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

Divide $z$ by $1$ .

$z = \frac{- 12}{3}$

$x = \frac{18 + z}{7}$

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

$z = \frac{- 12}{3}$

$x = \frac{18 + z}{7}$

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

$z = \frac{- 12}{3}$

$x = \frac{18 + z}{7}$

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

Simplify the right side.

Divide $- 12$ by $3$ .

$z = - 4$

$x = \frac{18 + z}{7}$

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

$z = - 4$

$x = \frac{18 + z}{7}$

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

$z = - 4$

$x = \frac{18 + z}{7}$

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

$z = - 4$

$x = \frac{18 + z}{7}$

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

Step 6

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

Replace all occurrences of $z$ in $x = \frac{18 + z}{7}$ with $- 4$ .

$x = \frac{18 - 4}{7}$

$z = - 4$

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

Simplify $x = \frac{18 - 4}{7}$ .

Simplify the left side.

Remove parentheses.

$x = \frac{18 - 4}{7}$

$z = - 4$

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

$x = \frac{18 - 4}{7}$

$z = - 4$

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

Simplify the right side.

Simplify $\frac{18 - 4}{7}$ .

Subtract $4$ from $18$ .

$x = \frac{14}{7}$

$z = - 4$

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

Divide $14$ by $7$ .

$x = 2$

$z = - 4$

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

$x = 2$

$z = - 4$

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

$x = 2$

$z = - 4$

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

$x = 2$

$z = - 4$

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

Replace all occurrences of $z$ in $y = - \frac{10}{7} + \frac{z}{7}$ with $- 4$ .

$y = - \frac{10}{7} + \frac{- 4}{7}$

$x = 2$

$z = - 4$

Simplify the right side.

Simplify $- \frac{10}{7} + \frac{- 4}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 10 - 4}{7}$

$x = 2$

$z = - 4$

Simplify the expression.

Subtract $4$ from $- 10$ .

$y = \frac{- 14}{7}$

$x = 2$

$z = - 4$

Divide $- 14$ by $7$ .

$y = - 2$

$x = 2$

$z = - 4$

$y = - 2$

$x = 2$

$z = - 4$

$y = - 2$

$x = 2$

$z = - 4$

$y = - 2$

$x = 2$

$z = - 4$

$y = - 2$

$x = 2$

$z = - 4$

Step 7

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

$(2, - 2, - 4)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(2, - 2, - 4)$

Equation Form:

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

Solve the System of Equations -3x+4y-z=-10 x+6y-z=-6 -2x-5y+z=2

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