Precalculus Examples

$- 5 x - y + z = 9$ , $z = 2 x + 4 y - 15$ , $y = x + 8$

Step 1

Replace all occurrences of $z$ with $2 x + 4 y - 15$ in each equation.

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Step 1.1

Replace all occurrences of $z$ in $- 5 x - y + z = 9$ with $2 x + 4 y - 15$ .

$- 5 x - y + 2 x + 4 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $- 5 x - y + 2 x + 4 y - 15$ .

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Step 1.2.1.1

Remove parentheses.

$- 5 x - y + 2 x + 4 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 1.2.1.2

Add $- 5 x$ and $2 x$ .

$- 3 x - y + 4 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 1.2.1.3

Add $- y$ and $4 y$ .

$- 3 x + 3 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$- 3 x + 3 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$- 3 x + 3 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$- 3 x + 3 y - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2

Replace all occurrences of $y$ with $x + 8$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 3 x + 3 y - 15 = 9$ with $x + 8$ .

$- 3 x + 3 (x + 8) - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 x + 3 (x + 8) - 15$ .

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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.

$- 3 x + 3 x + 3 \cdot 8 - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.2.1.1.2

Multiply $3$ by $8$ .

$- 3 x + 3 x + 24 - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$- 3 x + 3 x + 24 - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $- 3 x$ and $3 x$ .

$0 + 24 - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.2.1.2.2

Simplify by subtracting numbers.

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Step 2.2.1.2.2.1

Add $0$ and $24$ .

$24 - 15 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.2.1.2.2.2

Subtract $15$ from $24$ .

$9 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$9 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$9 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$9 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

$9 = 9$

$z = 2 x + 4 y - 15$

$y = x + 8$

Step 2.3

Replace all occurrences of $y$ in $z = 2 x + 4 y - 15$ with $x + 8$ .

$z = 2 x + 4 (x + 8) - 15$

$9 = 9$

$y = x + 8$

Step 2.4

Simplify the right side.

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Step 2.4.1

Simplify $2 x + 4 (x + 8) - 15$ .

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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.

$z = 2 x + 4 x + 4 \cdot 8 - 15$

$9 = 9$

$y = x + 8$

Step 2.4.1.1.2

Multiply $4$ by $8$ .

$z = 2 x + 4 x + 32 - 15$

$9 = 9$

$y = x + 8$

$z = 2 x + 4 x + 32 - 15$

$9 = 9$

$y = x + 8$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $2 x$ and $4 x$ .

$z = 6 x + 32 - 15$

$9 = 9$

$y = x + 8$

Step 2.4.1.2.2

Subtract $15$ from $32$ .

$z = 6 x + 17$

$9 = 9$

$y = x + 8$

$z = 6 x + 17$

$9 = 9$

$y = x + 8$

$z = 6 x + 17$

$9 = 9$

$y = x + 8$

$z = 6 x + 17$

$9 = 9$

$y = x + 8$

$z = 6 x + 17$

$9 = 9$

$y = x + 8$

Step 3

Remove any equations from the system that are always true.

$z = 6 x + 17$

$y = x + 8$