Answer
The solution set is $\{(2-t,t)\ |\ t\in \mathbb{R}\}$
Work Step by Step
Equation 1 variable x isolated - select the substitution method.
$x=2-y\qquad $(*)
Replace $x$ with $2-y$ in the second equation:
$ 3(2-y)+3y=6\qquad$ ... and solve for $x$. Simplify
$6-3y+3y=6$
$ 6=6\qquad$ ... always true, infinitely many solutions.
This is the case where both equations have graphs that coincide.
All points on that common line have coordinates that satisfy both equations.
Letting $y=t\in \mathbb{R}$ (be any real number), from equation 1 it follows:
$x=2-t$
The solution set is $\{(2-t,t)\ |\ t\in \mathbb{R}\}$
