Answer
The system of linear equations has infinitely many solutions.
Work Step by Step
The given system of equations is
$x+y=3$ ...... (1)
$2x+2y=6$ ...... (2)
Multiply equation (1) by $-2$.
$-2(x+y)=-2(3)$
Use distributive property.
$-2x-2y=-6$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 2x+2y-2x-2y=6-6$
Add like terms.
$\Rightarrow 0=0$
The equation $0=0$ is always true.
Hence, the system of linear equations has infinitely many solutions.
