Algebra Examples

$- 8 x + y + 2 z = - 7$ $x + y + 5 z = - 10$ $3 x - y + z = - 10$

Step 1

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

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Step 1.1

Add $8 x$ to both sides of the equation.

$y + 2 z = - 7 + 8 x$

$x + y + 5 z = - 10$

$3 x - y + z = - 10$

Step 1.2

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

$y = - 7 + 8 x - 2 z$

$x + y + 5 z = - 10$

$3 x - y + z = - 10$

$y = - 7 + 8 x - 2 z$

$x + y + 5 z = - 10$

$3 x - y + z = - 10$

Step 2

Replace all occurrences of $y$ with $- 7 + 8 x - 2 z$ in each equation.

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Step 2.1

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

$x - 7 + 8 x - 2 z + 5 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x - 7 + 8 x - 2 z + 5 z$ .

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Step 2.2.1.1

Remove parentheses.

$x - 7 + 8 x - 2 z + 5 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

Step 2.2.1.2

Add $x$ and $8 x$ .

$9 x - 7 - 2 z + 5 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

Step 2.2.1.3

Add $- 2 z$ and $5 z$ .

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x - y + z = - 10$

Step 2.3

Replace all occurrences of $y$ in $3 x - y + z = - 10$ with $- 7 + 8 x - 2 z$ .

$3 x - (- 7 + 8 x - 2 z) + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 x - (- 7 + 8 x - 2 z) + z$ .

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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.

$3 x + 7 - (8 x) - (- 2 z) + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $- 1$ by $- 7$ .

$3 x + 7 - (8 x) - (- 2 z) + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4.1.1.2.2

Multiply $8$ by $- 1$ .

$3 x + 7 - 8 x - (- 2 z) + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4.1.1.2.3

Multiply $- 2$ by $- 1$ .

$3 x + 7 - 8 x + 2 z + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x + 7 - 8 x + 2 z + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$3 x + 7 - 8 x + 2 z + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Subtract $8 x$ from $3 x$ .

$- 5 x + 7 + 2 z + z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 2.4.1.2.2

Add $2 z$ and $z$ .

$- 5 x + 7 + 3 z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$- 5 x + 7 + 3 z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$- 5 x + 7 + 3 z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$- 5 x + 7 + 3 z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$- 5 x + 7 + 3 z = - 10$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3

Solve for $x$ in $- 5 x + 7 + 3 z = - 10$ .

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Step 3.1

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

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Step 3.1.1

Subtract $7$ from both sides of the equation.

$- 5 x + 3 z = - 10 - 7$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.1.2

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

$- 5 x = - 10 - 7 - 3 z$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.1.3

Subtract $7$ from $- 10$ .

$- 5 x = - 17 - 3 z$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$- 5 x = - 17 - 3 z$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.2

Divide each term in $- 5 x = - 17 - 3 z$ by $- 5$ and simplify.

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Step 3.2.1

Divide each term in $- 5 x = - 17 - 3 z$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 17}{- 5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 17}{- 5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 17}{- 5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{- 17}{- 5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{- 17}{- 5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

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

Dividing two negative values results in a positive value.

$x = \frac{17}{5} + \frac{- 3 z}{- 5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 3.2.3.1.2

Dividing two negative values results in a positive value.

$x = \frac{17}{5} + \frac{3 z}{5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{17}{5} + \frac{3 z}{5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{17}{5} + \frac{3 z}{5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{17}{5} + \frac{3 z}{5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

$x = \frac{17}{5} + \frac{3 z}{5}$

$9 x - 7 + 3 z = - 10$

$y = - 7 + 8 x - 2 z$

Step 4

Replace all occurrences of $x$ with $\frac{17}{5} + \frac{3 z}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $9 x - 7 + 3 z = - 10$ with $\frac{17}{5} + \frac{3 z}{5}$ .

$9 (\frac{17}{5} + \frac{3 z}{5}) - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $9 (\frac{17}{5} + \frac{3 z}{5}) - 7 + 3 z$ .

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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.

$9 (\frac{17}{5}) + 9 (\frac{3 z}{5}) - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.1.2

Multiply $9 (\frac{17}{5})$ .

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Step 4.2.1.1.2.1

Combine $9$ and $\frac{17}{5}$ .

$\frac{9 \cdot 17}{5} + 9 (\frac{3 z}{5}) - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.1.2.2

Multiply $9$ by $17$ .

$\frac{153}{5} + 9 (\frac{3 z}{5}) - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{153}{5} + 9 (\frac{3 z}{5}) - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.1.3

Multiply $9 \frac{3 z}{5}$ .

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Step 4.2.1.1.3.1

Combine $9$ and $\frac{3 z}{5}$ .

$\frac{153}{5} + \frac{9 (3 z)}{5} - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.1.3.2

Multiply $3$ by $9$ .

$\frac{153}{5} + \frac{27 z}{5} - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{153}{5} + \frac{27 z}{5} - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{153}{5} + \frac{27 z}{5} - 7 + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.2

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

$\frac{27 z}{5} + \frac{153}{5} - 7 \cdot \frac{5}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.3

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

$\frac{27 z}{5} + \frac{153}{5} + \frac{- 7 \cdot 5}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{27 z}{5} + \frac{153 - 7 \cdot 5}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $- 7$ by $5$ .

$\frac{27 z}{5} + \frac{153 - 35}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.5.2

Subtract $35$ from $153$ .

$\frac{27 z}{5} + \frac{118}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{27 z}{5} + \frac{118}{5} + 3 z = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.6

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

$\frac{27 z}{5} + 3 z \cdot \frac{5}{5} + \frac{118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.7

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

$\frac{27 z}{5} + \frac{3 z \cdot 5}{5} + \frac{118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.8

Combine the numerators over the common denominator.

$\frac{27 z + 3 z \cdot 5}{5} + \frac{118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.9

Combine the numerators over the common denominator.

$\frac{27 z + 3 z \cdot 5 + 118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.10

Multiply $5$ by $3$ .

$\frac{27 z + 15 z + 118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.11

Add $27 z$ and $15 z$ .

$\frac{42 z + 118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.12

Factor $2$ out of $42 z + 118$ .

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Step 4.2.1.12.1

Factor $2$ out of $42 z$ .

$\frac{2 (21 z) + 118}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.12.2

Factor $2$ out of $118$ .

$\frac{2 (21 z) + 2 (59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.2.1.12.3

Factor $2$ out of $2 (21 z) + 2 (59)$ .

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + 8 x - 2 z$

Step 4.3

Replace all occurrences of $x$ in $y = - 7 + 8 x - 2 z$ with $\frac{17}{5} + \frac{3 z}{5}$ .

$y = - 7 + 8 (\frac{17}{5} + \frac{3 z}{5}) - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $- 7 + 8 (\frac{17}{5} + \frac{3 z}{5}) - 2 z$ .

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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.

$y = - 7 + 8 (\frac{17}{5}) + 8 (\frac{3 z}{5}) - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.1.2

Multiply $8 (\frac{17}{5})$ .

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Step 4.4.1.1.2.1

Combine $8$ and $\frac{17}{5}$ .

$y = - 7 + \frac{8 \cdot 17}{5} + 8 (\frac{3 z}{5}) - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.1.2.2

Multiply $8$ by $17$ .

$y = - 7 + \frac{136}{5} + 8 (\frac{3 z}{5}) - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + \frac{136}{5} + 8 (\frac{3 z}{5}) - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.1.3

Multiply $8 \frac{3 z}{5}$ .

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Step 4.4.1.1.3.1

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

$y = - 7 + \frac{136}{5} + \frac{8 (3 z)}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.1.3.2

Multiply $3$ by $8$ .

$y = - 7 + \frac{136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + \frac{136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = - 7 + \frac{136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.2

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

$y = - 7 \cdot \frac{5}{5} + \frac{136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.3

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

$y = \frac{- 7 \cdot 5}{5} + \frac{136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$y = \frac{- 7 \cdot 5 + 136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $- 7$ by $5$ .

$y = \frac{- 35 + 136}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.5.2

Add $- 35$ and $136$ .

$y = \frac{101}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = \frac{101}{5} + \frac{24 z}{5} - 2 z$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.6

To write $- 2 z$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{101}{5} + \frac{24 z}{5} - 2 z \cdot \frac{5}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.7

Combine $- 2 z$ and $\frac{5}{5}$ .

$y = \frac{101}{5} + \frac{24 z}{5} + \frac{- 2 z \cdot 5}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$y = \frac{101}{5} + \frac{24 z - 2 z \cdot 5}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$y = \frac{101 + 24 z - 2 z \cdot 5}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.10

Multiply $5$ by $- 2$ .

$y = \frac{101 + 24 z - 10 z}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 4.4.1.11

Subtract $10 z$ from $24 z$ .

$y = \frac{101 + 14 z}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = \frac{101 + 14 z}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = \frac{101 + 14 z}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = \frac{101 + 14 z}{5}$

$\frac{2 (21 z + 59)}{5} = - 10$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5

Solve for $z$ in $\frac{2 (21 z + 59)}{5} = - 10$ .

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Step 5.1

Multiply both sides by $5$ .

$\frac{2 (21 z + 59)}{5} \cdot 5 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2

Simplify.

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Step 5.2.1

Simplify the left side.

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Step 5.2.1.1

Simplify $\frac{2 (21 z + 59)}{5} \cdot 5$ .

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Step 5.2.1.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1.1

Cancel the common factor.

$\frac{2 (21 z + 59)}{5} \cdot 5 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2.1.1.1.2

Rewrite the expression.

$2 (21 z + 59) = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$2 (21 z + 59) = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2.1.1.2

Apply the distributive property.

$2 (21 z) + 2 \cdot 59 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2.1.1.3

Multiply.

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Step 5.2.1.1.3.1

Multiply $21$ by $2$ .

$42 z + 2 \cdot 59 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2.1.1.3.2

Multiply $2$ by $59$ .

$42 z + 118 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z + 118 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z + 118 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z + 118 = - 10 \cdot 5$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $- 10$ by $5$ .

$42 z + 118 = - 50$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z + 118 = - 50$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z + 118 = - 50$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3

Solve for $z$ .

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Step 5.3.1

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

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Step 5.3.1.1

Subtract $118$ from both sides of the equation.

$42 z = - 50 - 118$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3.1.2

Subtract $118$ from $- 50$ .

$42 z = - 168$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$42 z = - 168$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3.2

Divide each term in $42 z = - 168$ by $42$ and simplify.

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Step 5.3.2.1

Divide each term in $42 z = - 168$ by $42$ .

$\frac{42 z}{42} = \frac{- 168}{42}$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3.2.2

Simplify the left side.

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Step 5.3.2.2.1

Cancel the common factor of $42$ .

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Step 5.3.2.2.1.1

Cancel the common factor.

$\frac{42 z}{42} = \frac{- 168}{42}$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 168}{42}$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = \frac{- 168}{42}$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = \frac{- 168}{42}$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 5.3.2.3

Simplify the right side.

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Step 5.3.2.3.1

Divide $- 168$ by $42$ .

$z = - 4$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = - 4$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = - 4$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = - 4$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

$z = - 4$

$y = \frac{101 + 14 z}{5}$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 6

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

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Step 6.1

Replace all occurrences of $z$ in $y = \frac{101 + 14 z}{5}$ with $- 4$ .

$y = \frac{101 + 14 (- 4)}{5}$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{101 + 14 (- 4)}{5}$ .

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Multiply $14$ by $- 4$ .

$y = \frac{101 - 56}{5}$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 6.2.1.1.2

Subtract $56$ from $101$ .

$y = \frac{45}{5}$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = \frac{45}{5}$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 6.2.1.2

Divide $45$ by $5$ .

$y = 9$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = 9$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

$y = 9$

$z = - 4$

$x = \frac{17}{5} + \frac{3 z}{5}$

Step 6.3

Replace all occurrences of $z$ in $x = \frac{17}{5} + \frac{3 z}{5}$ with $- 4$ .

$x = \frac{17}{5} + \frac{3 (- 4)}{5}$

$y = 9$

$z = - 4$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{17}{5} + \frac{3 (- 4)}{5}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$x = \frac{17 + 3 (- 4)}{5}$

$y = 9$

$z = - 4$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $3$ by $- 4$ .

$x = \frac{17 - 12}{5}$

$y = 9$

$z = - 4$

Step 6.4.1.2.2

Subtract $12$ from $17$ .

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

$y = 9$

$z = - 4$

Step 6.4.1.2.3

Divide $5$ by $5$ .

$x = 1$

$y = 9$

$z = - 4$

$x = 1$

$y = 9$

$z = - 4$

$x = 1$

$y = 9$

$z = - 4$

$x = 1$

$y = 9$

$z = - 4$

$x = 1$

$y = 9$

$z = - 4$

Step 7

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

$(1, 9, - 4)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(1, 9, - 4)$

Equation Form:

$x = 1, y = 9, z = - 4$