Solve the System of Equations y=-x+3 and 2x+2y=6

$y = - x + 3$ and $2 x + 2 y = 6$

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

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

$2 x + 2 (- x + 3) = 6$

$y = - x + 3$

Simplify the left side.

Simplify $2 x + 2 (- x + 3)$ .

Simplify each term.

Apply the distributive property.

$2 x + 2 (- x) + 2 \cdot 3 = 6$

$y = - x + 3$

Multiply $- 1$ by $2$ .

$2 x - 2 x + 2 \cdot 3 = 6$

$y = - x + 3$

Multiply $2$ by $3$ .

$2 x - 2 x + 6 = 6$

$y = - x + 3$

$2 x - 2 x + 6 = 6$

$y = - x + 3$

Simplify by adding terms.

Subtract $2 x$ from $2 x$ .

$0 + 6 = 6$

$y = - x + 3$

Add $0$ and $6$ .

$6 = 6$

$y = - x + 3$

$6 = 6$

$y = - x + 3$

$6 = 6$

$y = - x + 3$

$6 = 6$

$y = - x + 3$

$6 = 6$

$y = - x + 3$

Remove any equations from the system that are always true.

$y = - x + 3$

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