Finite Math Examples

$12 x + 4 y = 44$ , $y = 11 - 3 x$

Step 1

Reorder $11$ and $- 3 x$ .

$y = - 3 x + 11$

$12 x + 4 y = 44$

Step 2

Replace all occurrences of $y$ with $- 3 x + 11$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $12 x + 4 y = 44$ with $- 3 x + 11$ .

$12 x + 4 (- 3 x + 11) = 44$

$y = - 3 x + 11$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $12 x + 4 (- 3 x + 11)$ .

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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.

$12 x + 4 (- 3 x) + 4 \cdot 11 = 44$

$y = - 3 x + 11$

Step 2.2.1.1.2

Multiply $- 3$ by $4$ .

$12 x - 12 x + 4 \cdot 11 = 44$

$y = - 3 x + 11$

Step 2.2.1.1.3

Multiply $4$ by $11$ .

$12 x - 12 x + 44 = 44$

$y = - 3 x + 11$

$12 x - 12 x + 44 = 44$

$y = - 3 x + 11$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $12 x$ from $12 x$ .

$0 + 44 = 44$

$y = - 3 x + 11$

Step 2.2.1.2.2

Add $0$ and $44$ .

$44 = 44$

$y = - 3 x + 11$

$44 = 44$

$y = - 3 x + 11$

$44 = 44$

$y = - 3 x + 11$

$44 = 44$

$y = - 3 x + 11$

$44 = 44$

$y = - 3 x + 11$

Step 3

Remove any equations from the system that are always true.

$y = - 3 x + 11$

Step 4