Your equations are correct.

From equation 1, it is clear that x = y + 4.

So substitute this into equation 2 to get

1/(y + 4) - 1/y = 1/48

y/[y(y + 4)] - (y + 4)/[y(y + 4)] = 1/48

[y - (y + 4)]/[y(y + 4)] = 1/48

-4/[y(y + 4)] = 1/48

-4 = [y(y + 4)]/48

-192 = y(y + 4)

Now expand and set the equation equal to 0 and solve the resulting quadratic.