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

$x + 2 y = 4$ $2 x + 4 y = 8$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 4 - 2 y$

$2 x + 4 y = 8$

Step 2

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

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

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

$x = 4 - 2 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = 4 - 2 y$

Multiply $2$ by $4$ .

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

$x = 4 - 2 y$

Multiply $- 2$ by $2$ .

$8 - 4 y + 4 y = 8$

$x = 4 - 2 y$

$8 - 4 y + 4 y = 8$

$x = 4 - 2 y$

Combine the opposite terms in $8 - 4 y + 4 y$ .

Add $- 4 y$ and $4 y$ .

$8 + 0 = 8$

$x = 4 - 2 y$

Add $8$ and $0$ .

$8 = 8$

$x = 4 - 2 y$

$8 = 8$

$x = 4 - 2 y$

$8 = 8$

$x = 4 - 2 y$

$8 = 8$

$x = 4 - 2 y$

$8 = 8$

$x = 4 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 - 2 y$

Step 4