Answer
The solution set is $\{(t, 2t-3)\ |\ t\in \mathbb{R}\}$
Work Step by Step
Variable $y$ is isolated in eq.$2$
$y=2x-3\qquad $(*)
Replace $y$ with $2x-3$ in the other equation:
$ 4x-2(2x-3)=6\qquad$ ... and solve for $x$. Simplify
$4x-4x+6=6$
$ 0=0\qquad$ ... always true, there are 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 $x=t\in \mathbb{R}$ (be any real number), from equation $(*)$ it follows:
$y=2t-3$
The solution set is $\{(t, 2t-3)\ |\ t\in \mathbb{R}\}$