Finite Math Examples

$x + 2 y + z = - 2$ , $5 x + 3 y - z = - 11$ , $x + 5 y + 3 z = - 5$

Step 1

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

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Step 1.1

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

$x + z = - 2 - 2 y$

$5 x + 3 y - z = - 11$

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

Step 1.2

Subtract $z$ from both sides of the equation.

$x = - 2 - 2 y - z$

$5 x + 3 y - z = - 11$

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

$x = - 2 - 2 y - z$

$5 x + 3 y - z = - 11$

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

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $5 x + 3 y - z = - 11$ with $- 2 - 2 y - z$ .

$5 (- 2 - 2 y - z) + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$5 \cdot - 2 + 5 (- 2 y) + 5 (- z) + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $5$ by $- 2$ .

$- 10 + 5 (- 2 y) + 5 (- z) + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2.1.1.2.2

Multiply $- 2$ by $5$ .

$- 10 - 10 y + 5 (- z) + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2.1.1.2.3

Multiply $- 1$ by $5$ .

$- 10 - 10 y - 5 z + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 10 y - 5 z + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 10 y - 5 z + 3 y - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $- 10 y$ and $3 y$ .

$- 10 - 7 y - 5 z - z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.2.1.2.2

Subtract $z$ from $- 5 z$ .

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

Step 2.3

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

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 2.4

Simplify the left side.

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Step 2.4.1

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

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Step 2.4.1.1

Add $- 2 y$ and $5 y$ .

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 2.4.1.2

Add $- z$ and $3 z$ .

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3

Solve for $y$ in $- 2 + 3 y + 2 z = - 5$ .

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Step 3.1

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

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Step 3.1.1

Add $2$ to both sides of the equation.

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.1.2

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

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.1.3

Add $- 5$ and $2$ .

$3 y = - 3 - 2 z$

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

$3 y = - 3 - 2 z$

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.2

Divide each term in $3 y = - 3 - 2 z$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 y = - 3 - 2 z$ by $3$ .

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Divide $- 3$ by $3$ .

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 3.2.3.1.2

Move the negative in front of the fraction.

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

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

$- 10 - 7 y - 6 z = - 11$

$x = - 2 - 2 y - z$

Step 4

Replace all occurrences of $y$ with $- 1 - \frac{2 z}{3}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- 10 - 7 y - 6 z = - 11$ with $- 1 - \frac{2 z}{3}$ .

$- 10 - 7 (- 1 - \frac{2 z}{3}) - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 10 - 7 (- 1 - \frac{2 z}{3}) - 6 z$ .

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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.

$- 10 - 7 \cdot - 1 - 7 (- \frac{2 z}{3}) - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.1.2

Multiply $- 7$ by $- 1$ .

$- 10 + 7 - 7 (- \frac{2 z}{3}) - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.1.3

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

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Step 4.2.1.1.3.1

Multiply $- 1$ by $- 7$ .

$- 10 + 7 + 7 (\frac{2 z}{3}) - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.1.3.2

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

$- 10 + 7 + \frac{7 (2 z)}{3} - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.1.3.3

Multiply $2$ by $7$ .

$- 10 + 7 + \frac{14 z}{3} - 6 z = - 11$

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

$x = - 2 - 2 y - z$

$- 10 + 7 + \frac{14 z}{3} - 6 z = - 11$

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

$x = - 2 - 2 y - z$

$- 10 + 7 + \frac{14 z}{3} - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.2

Add $- 10$ and $7$ .

$- 3 + \frac{14 z}{3} - 6 z = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.3

To write $- 6 z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 3 + \frac{14 z}{3} - 6 z \cdot \frac{3}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.4

Simplify terms.

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Step 4.2.1.4.1

Combine $- 6 z$ and $\frac{3}{3}$ .

$- 3 + \frac{14 z}{3} + \frac{- 6 z \cdot 3}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.4.2

Combine the numerators over the common denominator.

$- 3 + \frac{14 z - 6 z \cdot 3}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 + \frac{14 z - 6 z \cdot 3}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5

Simplify each term.

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Step 4.2.1.5.1

Simplify the numerator.

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Step 4.2.1.5.1.1

Factor $2 z$ out of $14 z - 6 z \cdot 3$ .

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Step 4.2.1.5.1.1.1

Factor $2 z$ out of $14 z$ .

$- 3 + \frac{2 z (7) - 6 z \cdot 3}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.1.1.2

Factor $2 z$ out of $- 6 z \cdot 3$ .

$- 3 + \frac{2 z (7) + 2 z (- 3 \cdot 3)}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.1.1.3

Factor $2 z$ out of $2 z (7) + 2 z (- 3 \cdot 3)$ .

$- 3 + \frac{2 z (7 - 3 \cdot 3)}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 + \frac{2 z (7 - 3 \cdot 3)}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.1.2

Multiply $- 3$ by $3$ .

$- 3 + \frac{2 z (7 - 9)}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.1.3

Subtract $9$ from $7$ .

$- 3 + \frac{2 z \cdot - 2}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.1.4

Multiply $- 2$ by $2$ .

$- 3 + \frac{- 4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 + \frac{- 4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.2.1.5.2

Move the negative in front of the fraction.

$- 3 - \frac{4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = - 2 - 2 y - z$

Step 4.3

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

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4

Simplify the right side.

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Step 4.4.1

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

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Apply the distributive property.

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.1.2

Multiply $- 2$ by $- 1$ .

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.1.3

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

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 2$ .

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.1.3.2

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

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.1.3.3

Multiply $2$ by $2$ .

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

$- 3 - \frac{4 z}{3} = - 11$

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

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

$- 3 - \frac{4 z}{3} = - 11$

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

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.2

Simplify by adding numbers.

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Step 4.4.1.2.1

Add $- 2$ and $2$ .

$x = 0 + \frac{4 z}{3} - z$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.2.2

Add $0$ and $\frac{4 z}{3}$ .

$x = \frac{4 z}{3} - z$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{4 z}{3} - z$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.3

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

$x = \frac{4 z}{3} - z \cdot \frac{3}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.4

Simplify terms.

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Step 4.4.1.4.1

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

$x = \frac{4 z}{3} + \frac{- z \cdot 3}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.4.2

Combine the numerators over the common denominator.

$x = \frac{4 z - z \cdot 3}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{4 z - z \cdot 3}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Factor $z$ out of $4 z - z \cdot 3$ .

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Step 4.4.1.5.1.1

Factor $z$ out of $4 z$ .

$x = \frac{z \cdot 4 - z \cdot 3}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.5.1.2

Factor $z$ out of $- z \cdot 3$ .

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.5.1.3

Factor $z$ out of $z \cdot 4 + z (- 1 \cdot 3)$ .

$x = \frac{z (4 - 1 \cdot 3)}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{z (4 - 1 \cdot 3)}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.5.2

Multiply $- 1$ by $3$ .

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

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.5.3

Subtract $3$ from $4$ .

$x = \frac{z \cdot 1}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{z \cdot 1}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 4.4.1.6

Multiply $z$ by $1$ .

$x = \frac{z}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{z}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{z}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

$x = \frac{z}{3}$

$- 3 - \frac{4 z}{3} = - 11$

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

Step 5

Solve for $z$ in $- 3 - \frac{4 z}{3} = - 11$ .

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Step 5.1

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

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Step 5.1.1

Add $3$ to both sides of the equation.

$- \frac{4 z}{3} = - 11 + 3$

$x = \frac{z}{3}$

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

Step 5.1.2

Add $- 11$ and $3$ .

$- \frac{4 z}{3} = - 8$

$x = \frac{z}{3}$

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

$- \frac{4 z}{3} = - 8$

$x = \frac{z}{3}$

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

Step 5.2

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} \cdot (- \frac{4 z}{3}) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3

Simplify both sides of the equation.

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Step 5.3.1

Simplify the left side.

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Step 5.3.1.1

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

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Step 5.3.1.1.1

Cancel the common factor of $3$ .

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Step 5.3.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot (- \frac{4 z}{3}) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.1.2

Move the leading negative in $- \frac{4 z}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} \cdot (- 4 z) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

$\frac{- 1}{4} \cdot (- 4 z) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.2

Cancel the common factor of $4$ .

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Step 5.3.1.1.2.1

Factor $4$ out of $- 4 z$ .

$\frac{- 1}{4} \cdot (4 (- z)) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 (- z)) = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.2.3

Rewrite the expression.

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.3

Multiply.

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Step 5.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

$z = - \frac{3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.2

Simplify the right side.

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Step 5.3.2.1

Simplify $- \frac{3}{4} \cdot - 8$ .

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Step 5.3.2.1.1

Cancel the common factor of $4$ .

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Step 5.3.2.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$z = \frac{- 3}{4} \cdot - 8$

$x = \frac{z}{3}$

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

Step 5.3.2.1.1.2

Factor $4$ out of $- 8$ .

$z = \frac{- 3}{4} \cdot (4 (- 2))$

$x = \frac{z}{3}$

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

Step 5.3.2.1.1.3

Cancel the common factor.

$z = \frac{- 3}{4} \cdot (4 \cdot - 2)$

$x = \frac{z}{3}$

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

Step 5.3.2.1.1.4

Rewrite the expression.

$z = - 3 \cdot - 2$

$x = \frac{z}{3}$

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

$z = - 3 \cdot - 2$

$x = \frac{z}{3}$

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

Step 5.3.2.1.2

Multiply $- 3$ by $- 2$ .

$z = 6$

$x = \frac{z}{3}$

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

$z = 6$

$x = \frac{z}{3}$

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

$z = 6$

$x = \frac{z}{3}$

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

$z = 6$

$x = \frac{z}{3}$

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

$z = 6$

$x = \frac{z}{3}$

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

Step 6

Replace all occurrences of $z$ with $6$ in each equation.

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Step 6.1

Replace all occurrences of $z$ in $x = \frac{z}{3}$ with $6$ .

$x = \frac{6}{3}$

$z = 6$

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Divide $6$ by $3$ .

$x = 2$

$z = 6$

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

$x = 2$

$z = 6$

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

Step 6.3

Replace all occurrences of $z$ in $y = - 1 - \frac{2 z}{3}$ with $6$ .

$y = - 1 - \frac{2 (6)}{3}$

$x = 2$

$z = 6$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $- 1 - \frac{2 (6)}{3}$ .

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Step 6.4.1.1

Simplify each term.

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Step 6.4.1.1.1

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

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Step 6.4.1.1.1.1

Factor $3$ out of $2 (6)$ .

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

$x = 2$

$z = 6$

Step 6.4.1.1.1.2

Cancel the common factors.

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Step 6.4.1.1.1.2.1

Factor $3$ out of $3$ .

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

$x = 2$

$z = 6$

Step 6.4.1.1.1.2.2

Cancel the common factor.

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

$x = 2$

$z = 6$

Step 6.4.1.1.1.2.3

Rewrite the expression.

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

$x = 2$

$z = 6$

Step 6.4.1.1.1.2.4

Divide $2 \cdot (2)$ by $1$ .

$y = - 1 - (2 \cdot (2))$

$x = 2$

$z = 6$

$y = - 1 - (2 \cdot (2))$

$x = 2$

$z = 6$

$y = - 1 - (2 \cdot (2))$

$x = 2$

$z = 6$

Step 6.4.1.1.2

Multiply $- (2 \cdot (2))$ .

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Step 6.4.1.1.2.1

Multiply $2$ by $2$ .

$y = - 1 - 1 \cdot 4$

$x = 2$

$z = 6$

Step 6.4.1.1.2.2

Multiply $- 1$ by $4$ .

$y = - 1 - 4$

$x = 2$

$z = 6$

$y = - 1 - 4$

$x = 2$

$z = 6$

$y = - 1 - 4$

$x = 2$

$z = 6$

Step 6.4.1.2

Subtract $4$ from $- 1$ .

$y = - 5$

$x = 2$

$z = 6$

$y = - 5$

$x = 2$

$z = 6$

$y = - 5$

$x = 2$

$z = 6$

$y = - 5$

$x = 2$

$z = 6$

Step 7

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

$(2, - 5, 6)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(2, - 5, 6)$

Equation Form:

$x = 2, y = - 5, z = 6$