To solve this system of equations, we can use the method of substitution or elimination.

Let's solve it using the method of substitution.

First, we solve the first equation for y:
1/4x - y = 5
y = 1/4x - 5

Next, we substitute this expression for y into the second equation:
1/2x - 1/7(1/4x - 5) = 3
1/2x - 1/28x + 5/7 = 3
(7/14)x - (1/28)x + 5/7 = 3
(6/28)x + 5/7 = 3
(6/28)x = 3 - 5/7
(6/28)x = 21/7 - 5/7
(6/28)x = 16/7
x = (16/7) * (28/6)
x = 64/3
x = 21 1/3

Now, we can substitute the value of x back into the first equation to find the value of y:
1/4(21 1/3) - y = 5
(21 1/12) - y = 5
y = 21 1/12 - 5
y = 16 1/12
y = 49/3

Therefore, the solution to the system of equations is x = 21 1/3 and y = 16 1/12 (or 49/3).