5x - 2y = 17
4x - 3y = 8
Try to change one of the equations to isolate a variable, so you can use the new equation and substitute it into the other equation.
5x - 2y = 17
-2y = 17 - 5x
y = -17/2 + 5/2x
Now plug this into the second equation
4x - 3(-17/2 + 5/2x) = 8
4x + 51/2 - 15/2x = 8
8/2x - 15/2x = 16/2 - 51/2
-7/2x = -35/2
x = 5
Plug this into either equation to find y
4x - 3y = 8
4(5) - 3y = 8
20 - 3y = 8
-3y = -12
y = 4
x = 5, y = 4