Algebra Examples

$- 3 x - 6 y + 4 z = - 8$ $- 3 x - y + 2 z = 10$ $3 x + 4 y - 3 z = 1$

Step 1

Solve for $x$ in $- 3 x - 6 y + 4 z = - 8$ .

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Step 1.1

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

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Step 1.1.1

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

$- 3 x + 4 z = - 8 + 6 y$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.1.2

Subtract $4 z$ from both sides of the equation.

$- 3 x = - 8 + 6 y - 4 z$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$- 3 x = - 8 + 6 y - 4 z$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2

Divide each term in $- 3 x = - 8 + 6 y - 4 z$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 x = - 8 + 6 y - 4 z$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 8}{- 3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 8}{- 3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{- 8}{- 3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{- 8}{- 3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{8}{3} + \frac{6 y}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3.1.2

Cancel the common factor of $6$ and $- 3$ .

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Step 1.2.3.1.2.1

Factor $3$ out of $6 y$ .

$x = \frac{8}{3} + \frac{3 (2 y)}{- 3} + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3.1.2.2

Move the negative one from the denominator of $\frac{2 y}{- 1}$ .

$x = \frac{8}{3} - 1 \cdot (2 y) + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{8}{3} - 1 \cdot (2 y) + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (2 y)$ as $- (2 y)$ .

$x = \frac{8}{3} - (2 y) + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3.1.4

Multiply $2$ by $- 1$ .

$x = \frac{8}{3} - 2 y + \frac{- 4 z}{- 3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 1.2.3.1.5

Dividing two negative values results in a positive value.

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 3 x - y + 2 z = 10$

$3 x + 4 y - 3 z = 1$

Step 2

Replace all occurrences of $x$ with $\frac{8}{3} - 2 y + \frac{4 z}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 3 x - y + 2 z = 10$ with $\frac{8}{3} - 2 y + \frac{4 z}{3}$ .

$- 3 (\frac{8}{3} - 2 y + \frac{4 z}{3}) - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 (\frac{8}{3} - 2 y + \frac{4 z}{3}) - y + 2 z$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- 3 (\frac{8}{3}) - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1.1

Factor $3$ out of $- 3$ .

$3 (- 1) (\frac{8}{3}) - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.1.2

Cancel the common factor.

$3 \cdot (- 1 (\frac{8}{3})) - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.1.3

Rewrite the expression.

$- 1 \cdot 8 - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 1 \cdot 8 - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.2

Multiply $- 1$ by $8$ .

$- 8 - 3 (- 2 y) - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.3

Multiply $- 2$ by $- 3$ .

$- 8 + 6 y - 3 \frac{4 z}{3} - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.4

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.4.1

Factor $3$ out of $- 3$ .

$- 8 + 6 y + 3 (- 1) (\frac{4 z}{3}) - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.4.2

Cancel the common factor.

$- 8 + 6 y + 3 \cdot (- 1 \frac{4 z}{3}) - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.4.3

Rewrite the expression.

$- 8 + 6 y - 1 (4 z) - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 6 y - 1 (4 z) - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.1.2.5

Multiply $4$ by $- 1$ .

$- 8 + 6 y - 4 z - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 6 y - 4 z - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 6 y - 4 z - y + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $y$ from $6 y$ .

$- 8 + 5 y - 4 z + 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.2.1.2.2

Add $- 4 z$ and $2 z$ .

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$3 x + 4 y - 3 z = 1$

Step 2.3

Replace all occurrences of $x$ in $3 x + 4 y - 3 z = 1$ with $\frac{8}{3} - 2 y + \frac{4 z}{3}$ .

$3 (\frac{8}{3} - 2 y + \frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 (\frac{8}{3} - 2 y + \frac{4 z}{3}) + 4 y - 3 z$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$3 (\frac{8}{3}) + 3 (- 2 y) + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Cancel the common factor of $3$ .

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Step 2.4.1.1.2.1.1

Cancel the common factor.

$3 (\frac{8}{3}) + 3 (- 2 y) + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.1.2.1.2

Rewrite the expression.

$8 + 3 (- 2 y) + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 + 3 (- 2 y) + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.1.2.2

Multiply $- 2$ by $3$ .

$8 - 6 y + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.1.2.3

Cancel the common factor of $3$ .

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Step 2.4.1.1.2.3.1

Cancel the common factor.

$8 - 6 y + 3 (\frac{4 z}{3}) + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.1.2.3.2

Rewrite the expression.

$8 - 6 y + 4 z + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 6 y + 4 z + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 6 y + 4 z + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 6 y + 4 z + 4 y - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $- 6 y$ and $4 y$ .

$8 - 2 y + 4 z - 3 z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 2.4.1.2.2

Subtract $3 z$ from $4 z$ .

$8 - 2 y + z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 2 y + z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 2 y + z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 2 y + z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$8 - 2 y + z = 1$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the equation.

$- 2 y + z = 1 - 8$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 3.2

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

$z = 1 - 8 + 2 y$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 3.3

Subtract $8$ from $1$ .

$z = - 7 + 2 y$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$z = - 7 + 2 y$

$- 8 + 5 y - 2 z = 10$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4

Replace all occurrences of $z$ with $- 7 + 2 y$ in each equation.

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Step 4.1

Replace all occurrences of $z$ in $- 8 + 5 y - 2 z = 10$ with $- 7 + 2 y$ .

$- 8 + 5 y - 2 (- 7 + 2 y) = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 8 + 5 y - 2 (- 7 + 2 y)$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Apply the distributive property.

$- 8 + 5 y - 2 \cdot - 7 - 2 (2 y) = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.2.1.1.2

Multiply $- 2$ by $- 7$ .

$- 8 + 5 y + 14 - 2 (2 y) = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.2.1.1.3

Multiply $2$ by $- 2$ .

$- 8 + 5 y + 14 - 4 y = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$- 8 + 5 y + 14 - 4 y = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.2.1.2

Simplify by adding terms.

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Step 4.2.1.2.1

Add $- 8$ and $14$ .

$5 y + 6 - 4 y = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.2.1.2.2

Subtract $4 y$ from $5 y$ .

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{8}{3} - 2 y + \frac{4 z}{3}$

Step 4.3

Replace all occurrences of $z$ in $x = \frac{8}{3} - 2 y + \frac{4 z}{3}$ with $- 7 + 2 y$ .

$x = \frac{8}{3} - 2 y + \frac{4 (- 7 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $\frac{8}{3} - 2 y + \frac{4 (- 7 + 2 y)}{3}$ .

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Step 4.4.1.1

Combine the numerators over the common denominator.

$x = - 2 y + \frac{8 + 4 (- 7 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.2

Simplify each term.

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Step 4.4.1.2.1

Apply the distributive property.

$x = - 2 y + \frac{8 + 4 \cdot - 7 + 4 (2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.2.2

Multiply $4$ by $- 7$ .

$x = - 2 y + \frac{8 - 28 + 4 (2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.2.3

Multiply $2$ by $4$ .

$x = - 2 y + \frac{8 - 28 + 8 y}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = - 2 y + \frac{8 - 28 + 8 y}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.3

Simplify with factoring out.

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Step 4.4.1.3.1

Subtract $28$ from $8$ .

$x = - 2 y + \frac{- 20 + 8 y}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.3.2

Factor $4$ out of $- 20 + 8 y$ .

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Step 4.4.1.3.2.1

Factor $4$ out of $- 20$ .

$x = - 2 y + \frac{4 (- 5) + 8 y}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.3.2.2

Factor $4$ out of $8 y$ .

$x = - 2 y + \frac{4 (- 5) + 4 (2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.3.2.3

Factor $4$ out of $4 (- 5) + 4 (2 y)$ .

$x = - 2 y + \frac{4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = - 2 y + \frac{4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = - 2 y + \frac{4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.4

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - 2 y \cdot \frac{3}{3} + \frac{4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.5

Simplify terms.

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Step 4.4.1.5.1

Combine $- 2 y$ and $\frac{3}{3}$ .

$x = \frac{- 2 y \cdot 3}{3} + \frac{4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.5.2

Combine the numerators over the common denominator.

$x = \frac{- 2 y \cdot 3 + 4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{- 2 y \cdot 3 + 4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6

Simplify the numerator.

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Step 4.4.1.6.1

Factor $2$ out of $- 2 y \cdot 3 + 4 (- 5 + 2 y)$ .

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Step 4.4.1.6.1.1

Factor $2$ out of $- 2 y \cdot 3$ .

$x = \frac{2 (- y \cdot 3) + 4 (- 5 + 2 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.1.2

Factor $2$ out of $4 (- 5 + 2 y)$ .

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

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.1.3

Factor $2$ out of $2 (- y \cdot 3) + 2 (2 (- 5 + 2 y))$ .

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

$y + 6 = 10$

$z = - 7 + 2 y$

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

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.2

Multiply $3$ by $- 1$ .

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

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.3

Apply the distributive property.

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

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.4

Multiply $2$ by $- 5$ .

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

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.5

Multiply $2$ by $2$ .

$x = \frac{2 (- 3 y - 10 + 4 y)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 4.4.1.6.6

Add $- 3 y$ and $4 y$ .

$x = \frac{2 (y - 10)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{2 (y - 10)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{2 (y - 10)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{2 (y - 10)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

$x = \frac{2 (y - 10)}{3}$

$y + 6 = 10$

$z = - 7 + 2 y$

Step 5

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

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Step 5.1

Subtract $6$ from both sides of the equation.

$y = 10 - 6$

$x = \frac{2 (y - 10)}{3}$

$z = - 7 + 2 y$

Step 5.2

Subtract $6$ from $10$ .

$y = 4$

$x = \frac{2 (y - 10)}{3}$

$z = - 7 + 2 y$

$y = 4$

$x = \frac{2 (y - 10)}{3}$

$z = - 7 + 2 y$

Step 6

Replace all occurrences of $y$ with $4$ in each equation.

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Step 6.1

Replace all occurrences of $y$ in $x = \frac{2 (y - 10)}{3}$ with $4$ .

$x = \frac{2 ((4) - 10)}{3}$

$y = 4$

$z = - 7 + 2 y$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{2 ((4) - 10)}{3}$ .

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Step 6.2.1.1

Subtract $10$ from $4$ .

$x = \frac{2 \cdot - 6}{3}$

$y = 4$

$z = - 7 + 2 y$

Step 6.2.1.2

Multiply $2$ by $- 6$ .

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

$y = 4$

$z = - 7 + 2 y$

Step 6.2.1.3

Divide $- 12$ by $3$ .

$x = - 4$

$y = 4$

$z = - 7 + 2 y$

$x = - 4$

$y = 4$

$z = - 7 + 2 y$

$x = - 4$

$y = 4$

$z = - 7 + 2 y$

Step 6.3

Replace all occurrences of $y$ in $z = - 7 + 2 y$ with $4$ .

$z = - 7 + 2 (4)$

$x = - 4$

$y = 4$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $- 7 + 2 (4)$ .

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Step 6.4.1.1

Multiply $2$ by $4$ .

$z = - 7 + 8$

$x = - 4$

$y = 4$

Step 6.4.1.2

Add $- 7$ and $8$ .

$z = 1$

$x = - 4$

$y = 4$

$z = 1$

$x = - 4$

$y = 4$

$z = 1$

$x = - 4$

$y = 4$

$z = 1$

$x = - 4$

$y = 4$

Step 7

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

$(- 4, 4, 1)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 4, 4, 1)$

Equation Form:

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