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

$2 y - 4 x = - 4$ $y = - 2 + 2 x$

Step 1

Reorder $- 2$ and $2 x$ .

$y = 2 x - 2$

$2 y - 4 x = - 4$

Step 2

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

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

$2 (2 x - 2) - 4 x = - 4$

$y = 2 x - 2$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = 2 x - 2$

Multiply $2$ by $2$ .

$4 x + 2 \cdot - 2 - 4 x = - 4$

$y = 2 x - 2$

Multiply $2$ by $- 2$ .

$4 x - 4 - 4 x = - 4$

$y = 2 x - 2$

$4 x - 4 - 4 x = - 4$

$y = 2 x - 2$

Combine the opposite terms in $4 x - 4 - 4 x$ .

Subtract $4 x$ from $4 x$ .

$0 - 4 = - 4$

$y = 2 x - 2$

Subtract $4$ from $0$ .

$- 4 = - 4$

$y = 2 x - 2$

$- 4 = - 4$

$y = 2 x - 2$

$- 4 = - 4$

$y = 2 x - 2$

$- 4 = - 4$

$y = 2 x - 2$

$- 4 = - 4$

$y = 2 x - 2$

Step 3

Remove any equations from the system that are always true.

$y = 2 x - 2$

Step 4