Solve the simultaneous equations, 2x+4y = 1
3x-5y = 7

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)