Solve by Substitution y=2x-4 and 6x-3y=12

$y = 2 x - 4$ and $6 x - 3 y = 12$

Step 1

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

Replace all occurrences of $y$ in $6 x - 3 y = 12$ with $2 x - 4$ .

$6 x - 3 (2 x - 4) = 12$

$y = 2 x - 4$

Simplify the left side.

Simplify $6 x - 3 (2 x - 4)$ .

Simplify each term.

Apply the distributive property.

$6 x - 3 (2 x) - 3 \cdot - 4 = 12$

$y = 2 x - 4$

Multiply $2$ by $- 3$ .

$6 x - 6 x - 3 \cdot - 4 = 12$

$y = 2 x - 4$

Multiply $- 3$ by $- 4$ .

$6 x - 6 x + 12 = 12$

$y = 2 x - 4$

$6 x - 6 x + 12 = 12$

$y = 2 x - 4$

Simplify by adding terms.

Subtract $6 x$ from $6 x$ .

$0 + 12 = 12$

$y = 2 x - 4$

Add $0$ and $12$ .

$12 = 12$

$y = 2 x - 4$

$12 = 12$

$y = 2 x - 4$

$12 = 12$

$y = 2 x - 4$

$12 = 12$

$y = 2 x - 4$

$12 = 12$

$y = 2 x - 4$

Step 2

Remove any equations from the system that are always true.

$y = 2 x - 4$

Step 3

Related Questions