To find if the ordered pair is a solution for the equations, you plug the ordered pair into each equation as solve/Simplify.
2y + 3x = 4 (3/2,-1/4)
2(-1/4) + 3(3/2) = 4. Plug in and simplify
-2/4 + 9/2 = 4
8/2 = 4
4 = 4. The point is on the line
Plug the ordered pair into the second line:
5x = 8 + 2y
5(3/2) = 8 + 2(-1/4) plug in and simplify
15/2 = 8 + -2/4
7 1/2 = 7 1/2. The ordered pair is on that line
Since the point is on each of the lines, the point is part of the system. YES