I think you mean -2x+y=1 and 3y+2x=3.
Add the equations: 4y=4, so y=1 and -2x+y=-2x+1=1, -2x=0, x=0.
The solution to the system of equations is x=0, y=1, which is where the lines intersect,

The red line -2x+y=1 and the blue line 3y+2x=3. They intersect at (0,1).