Precalculus Examples

$y = 8 - 3 x$ , $9 x + 3 y = 24$

Step 1

Reorder $8$ and $- 3 x$ .

$y = - 3 x + 8$

$9 x + 3 y = 24$

Step 2

Replace all occurrences of $y$ with $- 3 x + 8$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $9 x + 3 y = 24$ with $- 3 x + 8$ .

$9 x + 3 (- 3 x + 8) = 24$

$y = - 3 x + 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $9 x + 3 (- 3 x + 8)$ .

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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.

$9 x + 3 (- 3 x) + 3 \cdot 8 = 24$

$y = - 3 x + 8$

Step 2.2.1.1.2

Multiply $- 3$ by $3$ .

$9 x - 9 x + 3 \cdot 8 = 24$

$y = - 3 x + 8$

Step 2.2.1.1.3

Multiply $3$ by $8$ .

$9 x - 9 x + 24 = 24$

$y = - 3 x + 8$

$9 x - 9 x + 24 = 24$

$y = - 3 x + 8$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $9 x$ from $9 x$ .

$0 + 24 = 24$

$y = - 3 x + 8$

Step 2.2.1.2.2

Add $0$ and $24$ .

$24 = 24$

$y = - 3 x + 8$

$24 = 24$

$y = - 3 x + 8$

$24 = 24$

$y = - 3 x + 8$

$24 = 24$

$y = - 3 x + 8$

$24 = 24$

$y = - 3 x + 8$

Step 3

Remove any equations from the system that are always true.

$y = - 3 x + 8$

Step 4