Solve the System of Equations 8x+4y=12 y=-2x+3

$8 x + 4 y = 12$ $y = - 2 x + 3$

Step 1

Replace all occurrences of $y$ with $- 2 x + 3$ in each equation.

Replace all occurrences of $y$ in $8 x + 4 y = 12$ with $- 2 x + 3$ .

$8 x + 4 (- 2 x + 3) = 12$

$y = - 2 x + 3$

Simplify the left side.

Simplify $8 x + 4 (- 2 x + 3)$ .

Simplify each term.

Apply the distributive property.

$8 x + 4 (- 2 x) + 4 \cdot 3 = 12$

$y = - 2 x + 3$

Multiply $- 2$ by $4$ .

$8 x - 8 x + 4 \cdot 3 = 12$

$y = - 2 x + 3$

Multiply $4$ by $3$ .

$8 x - 8 x + 12 = 12$

$y = - 2 x + 3$

$8 x - 8 x + 12 = 12$

$y = - 2 x + 3$

Simplify by adding terms.

Subtract $8 x$ from $8 x$ .

$0 + 12 = 12$

$y = - 2 x + 3$

Add $0$ and $12$ .

$12 = 12$

$y = - 2 x + 3$

$12 = 12$

$y = - 2 x + 3$

$12 = 12$

$y = - 2 x + 3$

$12 = 12$

$y = - 2 x + 3$

$12 = 12$

$y = - 2 x + 3$

Step 2

Remove any equations from the system that are always true.

$y = - 2 x + 3$

Step 3

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