Finite Math Examples

$- 8 x + 4 y = - 16$ , $y = 2 x - 4$

Step 1

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

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Step 1.1

Replace all occurrences of $y$ in $- 8 x + 4 y = - 16$ with $2 x - 4$ .

$- 8 x + 4 (2 x - 4) = - 16$

$y = 2 x - 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$- 8 x + 4 (2 x) + 4 \cdot - 4 = - 16$

$y = 2 x - 4$

Step 1.2.1.1.2

Multiply $2$ by $4$ .

$- 8 x + 8 x + 4 \cdot - 4 = - 16$

$y = 2 x - 4$

Step 1.2.1.1.3

Multiply $4$ by $- 4$ .

$- 8 x + 8 x - 16 = - 16$

$y = 2 x - 4$

$- 8 x + 8 x - 16 = - 16$

$y = 2 x - 4$

Step 1.2.1.2

Simplify by adding terms.

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Step 1.2.1.2.1

Add $- 8 x$ and $8 x$ .

$0 - 16 = - 16$

$y = 2 x - 4$

Step 1.2.1.2.2

Subtract $16$ from $0$ .

$- 16 = - 16$

$y = 2 x - 4$

$- 16 = - 16$

$y = 2 x - 4$

$- 16 = - 16$

$y = 2 x - 4$

$- 16 = - 16$

$y = 2 x - 4$

$- 16 = - 16$

$y = 2 x - 4$

Step 2

Remove any equations from the system that are always true.

$y = 2 x - 4$

Step 3