To solve this system of equations, we can use the method of substitution or elimination. Let's start by using the method of substitution:

1) Solve the first equation for y:
1/4x - y = -5
y = 1/4x + 5

2) Substitute y into the second equation:
1/2x - 1/7(1/4x + 5) = 3
1/2x - 1/28x - 5/7 = 3
(14/28)x - (1/28)x = 3 + 5/7
(13/28)x = 3 + 5/7
(13/28)x = 21/7 + 5/7
(13/28)x = 26/7
x = (26/7) * (28/13)
x = 52

3) Substitute x back into the first equation to solve for y:
1/4(52) - y = -5
13 - y = -5
y = 13 + 5
y = 18

Therefore, the solution to the system of equations is x = 52 and y = 18.