Solve by Substitution x-2y=3 , 4x-8y=12

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

Step 1

Add $2 y$ to both sides of the equation.

$x = 3 + 2 y$

$4 x - 8 y = 12$

Step 2

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

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

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

$x = 3 + 2 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = 3 + 2 y$

Multiply $4$ by $3$ .

$12 + 4 (2 y) - 8 y = 12$

$x = 3 + 2 y$

Multiply $2$ by $4$ .

$12 + 8 y - 8 y = 12$

$x = 3 + 2 y$

$12 + 8 y - 8 y = 12$

$x = 3 + 2 y$

Combine the opposite terms in $12 + 8 y - 8 y$ .

Subtract $8 y$ from $8 y$ .

$12 + 0 = 12$

$x = 3 + 2 y$

Add $12$ and $0$ .

$12 = 12$

$x = 3 + 2 y$

$12 = 12$

$x = 3 + 2 y$

$12 = 12$

$x = 3 + 2 y$

$12 = 12$

$x = 3 + 2 y$

$12 = 12$

$x = 3 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 3 + 2 y$

Step 4