Solve the System of Equations 3x+y-2z=-2 6x-4y+2z=2 12x-2y-2z=-2

$3 x + y - 2 z = - 2$ $6 x - 4 y + 2 z = 2$ $12 x - 2 y - 2 z = - 2$

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

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

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

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

$12 x - 2 y - 2 z = - 2$

Add $2 z$ to both sides of the equation.

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

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

$12 x - 2 y - 2 z = - 2$

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

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

$12 x - 2 y - 2 z = - 2$

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

Replace all occurrences of $y$ in $6 x - 4 y + 2 z = 2$ with $- 2 - 3 x + 2 z$ .

$6 x - 4 (- 2 - 3 x + 2 z) + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Simplify the left side.

Simplify $6 x - 4 (- 2 - 3 x + 2 z) + 2 z$ .

Simplify each term.

Apply the distributive property.

$6 x - 4 \cdot - 2 - 4 (- 3 x) - 4 (2 z) + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Simplify.

Multiply $- 4$ by $- 2$ .

$6 x + 8 - 4 (- 3 x) - 4 (2 z) + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Multiply $- 3$ by $- 4$ .

$6 x + 8 + 12 x - 4 (2 z) + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Multiply $2$ by $- 4$ .

$6 x + 8 + 12 x - 8 z + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

$6 x + 8 + 12 x - 8 z + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

$6 x + 8 + 12 x - 8 z + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Simplify by adding terms.

Add $6 x$ and $12 x$ .

$18 x + 8 - 8 z + 2 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Add $- 8 z$ and $2 z$ .

$18 x + 8 - 6 z = 2$

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

$12 x - 2 y - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

$12 x - 2 y - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

$12 x - 2 y - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

$12 x - 2 y - 2 z = - 2$

Replace all occurrences of $y$ in $12 x - 2 y - 2 z = - 2$ with $- 2 - 3 x + 2 z$ .

$12 x - 2 (- 2 - 3 x + 2 z) - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Simplify the left side.

Simplify $12 x - 2 (- 2 - 3 x + 2 z) - 2 z$ .

Simplify each term.

Apply the distributive property.

$12 x - 2 \cdot - 2 - 2 (- 3 x) - 2 (2 z) - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Simplify.

Multiply $- 2$ by $- 2$ .

$12 x + 4 - 2 (- 3 x) - 2 (2 z) - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Multiply $- 3$ by $- 2$ .

$12 x + 4 + 6 x - 2 (2 z) - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Multiply $2$ by $- 2$ .

$12 x + 4 + 6 x - 4 z - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

$12 x + 4 + 6 x - 4 z - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

$12 x + 4 + 6 x - 4 z - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Simplify by adding terms.

Add $12 x$ and $6 x$ .

$18 x + 4 - 4 z - 2 z = - 2$

$18 x + 8 - 6 z = 2$

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

Subtract $2 z$ from $- 4 z$ .

$18 x + 4 - 6 z = - 2$

$18 x + 8 - 6 z = 2$

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

$18 x + 4 - 6 z = - 2$

$18 x + 8 - 6 z = 2$

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

$18 x + 4 - 6 z = - 2$

$18 x + 8 - 6 z = 2$

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

$18 x + 4 - 6 z = - 2$

$18 x + 8 - 6 z = 2$

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

$18 x + 4 - 6 z = - 2$

$18 x + 8 - 6 z = 2$

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

Solve for $x$ in $18 x + 4 - 6 z = - 2$ .

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

Subtract $4$ from both sides of the equation.

$18 x - 6 z = - 2 - 4$

$18 x + 8 - 6 z = 2$

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

Add $6 z$ to both sides of the equation.

$18 x = - 2 - 4 + 6 z$

$18 x + 8 - 6 z = 2$

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

Subtract $4$ from $- 2$ .

$18 x = - 6 + 6 z$

$18 x + 8 - 6 z = 2$

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

$18 x = - 6 + 6 z$

$18 x + 8 - 6 z = 2$

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

Divide each term in $18 x = - 6 + 6 z$ by $18$ and simplify.

Divide each term in $18 x = - 6 + 6 z$ by $18$ .

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

$18 x + 8 - 6 z = 2$

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

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

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

$18 x + 8 - 6 z = 2$

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

Divide $x$ by $1$ .

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $18$ .

Factor $6$ out of $- 6$ .

$x = \frac{6 (- 1)}{18} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

Cancel the common factors.

Factor $6$ out of $18$ .

$x = \frac{6 \cdot - 1}{6 \cdot 3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

Cancel the common factor.

$x = \frac{6 \cdot - 1}{6 \cdot 3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

Rewrite the expression.

$x = \frac{- 1}{3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

$x = \frac{- 1}{3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

$x = \frac{- 1}{3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

Move the negative in front of the fraction.

$x = - \frac{1}{3} + \frac{6 z}{18}$

$18 x + 8 - 6 z = 2$

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

Cancel the common factor of $6$ and $18$ .

Factor $6$ out of $6 z$ .

$x = - \frac{1}{3} + \frac{6 (z)}{18}$

$18 x + 8 - 6 z = 2$

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

Cancel the common factors.

Factor $6$ out of $18$ .

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

$18 x + 8 - 6 z = 2$

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

Cancel the common factor.

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

$18 x + 8 - 6 z = 2$

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

Rewrite the expression.

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

$18 x + 8 - 6 z = 2$

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

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

Replace all occurrences of $x$ in $18 x + 8 - 6 z = 2$ with $- \frac{1}{3} + \frac{z}{3}$ .

$18 (- \frac{1}{3} + \frac{z}{3}) + 8 - 6 z = 2$

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

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

Simplify the left side.

Simplify $18 (- \frac{1}{3} + \frac{z}{3}) + 8 - 6 z$ .

Simplify each term.

Apply the distributive property.

$18 (- \frac{1}{3}) + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$18 (\frac{- 1}{3}) + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Factor $3$ out of $18$ .

$3 (6) (\frac{- 1}{3}) + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Cancel the common factor.

$3 \cdot (6 (\frac{- 1}{3})) + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Rewrite the expression.

$6 \cdot - 1 + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

$6 \cdot - 1 + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Multiply $6$ by $- 1$ .

$- 6 + 18 (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $18$ .

$- 6 + 3 (6) (\frac{z}{3}) + 8 - 6 z = 2$

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

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

Cancel the common factor.

$- 6 + 3 \cdot (6 (\frac{z}{3})) + 8 - 6 z = 2$

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

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

Rewrite the expression.

$- 6 + 6 z + 8 - 6 z = 2$

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

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

$- 6 + 6 z + 8 - 6 z = 2$

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

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

$- 6 + 6 z + 8 - 6 z = 2$

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

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

Simplify by adding terms.

Combine the opposite terms in $- 6 + 6 z + 8 - 6 z$ .

Subtract $6 z$ from $6 z$ .

$- 6 + 0 + 8 = 2$

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

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

Add $- 6$ and $0$ .

$- 6 + 8 = 2$

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

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

$- 6 + 8 = 2$

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

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

Add $- 6$ and $8$ .

$2 = 2$

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

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

$2 = 2$

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

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

$2 = 2$

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

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

$2 = 2$

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

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

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

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

$2 = 2$

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

Simplify the right side.

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

Simplify each term.

Apply the distributive property.

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

$2 = 2$

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

$2 = 2$

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

Factor $3$ out of $- 3$ .

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

$2 = 2$

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

Cancel the common factor.

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

$2 = 2$

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

Rewrite the expression.

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

$2 = 2$

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

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

$2 = 2$

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

Multiply $- 1$ by $- 1$ .

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

$2 = 2$

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

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

$2 = 2$

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

Cancel the common factor.

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

$2 = 2$

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

Rewrite the expression.

$y = - 2 + 1 - 1 z + 2 z$

$2 = 2$

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

$y = - 2 + 1 - 1 z + 2 z$

$2 = 2$

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

Rewrite $- 1 z$ as $- z$ .

$y = - 2 + 1 - z + 2 z$

$2 = 2$

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

$y = - 2 + 1 - z + 2 z$

$2 = 2$

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

Simplify by adding terms.

Add $- 2$ and $1$ .

$y = - 1 - z + 2 z$

$2 = 2$

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

Add $- z$ and $2 z$ .

$y = - 1 + z$

$2 = 2$

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

$y = - 1 + z$

$2 = 2$

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

$y = - 1 + z$

$2 = 2$

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

$y = - 1 + z$

$2 = 2$

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

$y = - 1 + z$

$2 = 2$

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

Remove any equations from the system that are always true.

$y = - 1 + z$

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

Solve the System of Equations 3x+y-2z=-2 6x-4y+2z=2 12x-2y-2z=-2

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