You have this
4x +7y = 60
-4x +7y = -4
just add the equations together
4x and -4x make 0x
7y and 7y make 14y
60 and -4 make 56
4x +7y = 60
-4x +7y = -4
0x +14y = 56
solve for y
0x +14y = 56
14y = 56
y = 4
now go back to the original equations
4x +7y = 60
-4x +7y = -4
multiply the bottom equation by -1 on both sides
4x +7y = 60
4x -7y = 4
add the equations together
8x +0y = 64
solve for x
8x + 0y = 64
8x = 64
x = 8
Answer: x = 8, y = 4