For a solution to exist the x and y values must be equal at that point.
I'll solve both for y first (and there are other ways to do this of course)
2x+4y=1, 4y=1-2x, y=(1-2x)/4
3x-5y=7, -5y=7-3x, y=(3x-7)/5
Since y=y at the solution point we can say:
(1-2x)/4=(3x-7)/5 cross multiplying...
5-10x=12x-28
-22x=-33
x=3/2 or if you prefer 1.5, now we can solve for y using either origianl equation...
2(1.5)+4y=1
3+4y=1
4y=-2
y=-0.5
So the solution is the point (1.5, -0.5)
