Solve the System of Equations 2x+2y=12 x+y=6

$2 x + 2 y = 12$ $x + y = 6$

Subtract $y$ from both sides of the equation.

$x = 6 - y$

$2 x + 2 y = 12$

Replace all occurrences of $x$ with $6 - y$ in each equation.

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

$2 (6 - y) + 2 y = 12$

$x = 6 - y$

Simplify the left side.

Simplify $2 (6 - y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 6 + 2 (- y) + 2 y = 12$

$x = 6 - y$

Multiply $2$ by $6$ .

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

$x = 6 - y$

Multiply $- 1$ by $2$ .

$12 - 2 y + 2 y = 12$

$x = 6 - y$

$12 - 2 y + 2 y = 12$

$x = 6 - y$

Combine the opposite terms in $12 - 2 y + 2 y$ .

Add $- 2 y$ and $2 y$ .

$12 + 0 = 12$

$x = 6 - y$

Add $12$ and $0$ .

$12 = 12$

$x = 6 - y$

$12 = 12$

$x = 6 - y$

$12 = 12$

$x = 6 - y$

$12 = 12$

$x = 6 - y$

$12 = 12$

$x = 6 - y$

Remove any equations from the system that are always true.

$x = 6 - y$

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