Answer
The system of linear equations has no solution.
Work Step by Step
The given system of equations is
$y=-x+3$ ...... (1)
$2x+2y=4$ ...... (2)
Multiply equation (1) by $-2$.
$-2(y)=-2(-x+3)$
Use distributive property.
$-2y=2x-6$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 2x+2y-2y=4+2x-6$
Add like terms.
$\Rightarrow 2x=2x-2$
Subtract $2x$ from each side.
$\Rightarrow 2x-2x=2x-2-2x$
Simplify.
$\Rightarrow 0=-2$
The equation $0=-2$ is never true.
Hence, the system of linear equations has no solution.
