2x + 7y = 4
-4x - 3y = 14
Well, looking at it, to me it would be easiest to multiply the top by 2 to get 4x, since 4x - 4x = 0.
4x + 14y = 8
-4x - 3y = 14
Now, if we add the two equations...
11y = 22
y = 2
Plug that into either equation.
2x + 7(2) = 4
2x + 14 = 4
2x = -10
x = -5
(-5,2)