We first focus on the first and last part of the equality.
(y - 2)/3 = 24/(y - 1)
(y - 2)(y - 1) = 72
y^2 - 3y + 2 - 72 = 0
y^2 - 3y - 70 = 0
(y - 10)(y + 7) = 0
y = 10 or y = -7
Case 1: y = 10
Then (10 - 2)/3 = (1 - 5x)/(10 - 4).
i.e., (1 - 5x)/6 = 8/3
(1 - 5x) = 16
x = -3
So (x, y) = (-3, 10) is a solution.
Case 2: y = -7
Then (-7 - 2)/3 = (1 - 5x)/(-7 - 4)
i.e., 1 - 5x = 33
x = -32/5
So (x, y) = (-32/5, -7) is another solution.