C. (8, -1)
For this problem, the easiest method is to simply try each of the 4 possible answers and see which one fits. So
A. (3, 9)
2x + 3y > 1
2*3 + 3*9 > 1 ; Obviously true, not going to finish calculation.
y < 5/4 x - 1
9 < 5/4 3 - 1
9 < 15/4 - 1 ; Obviously false, not going to finish calculation.
B. (-4, 2)
2x + 3y > 1
2*(-4) + 3*2 > 1
-8 + 6 > 1 ; Obviously false, not going to finish calculation.
No need to bother with 2nd inequality.
C. (8, -1)
2x + 3y > 1
2*8 + 3*(-1) > 1
16 - 3 > 1 ; Obviously true, not going to finish calculation.
y < 5/4 x - 1
-1 < 5/4 * 8 - 1
-1 < 40/4 - 1
-1 < 10 - 1 ; Obviously true, not going to finish calculation.
Both inequalities satisfied, this is the correct choice.
D. (-2, -5)
2x + 3y > 1
2*(-2) + 3*(-5) > 1; Left hand side is obviously negative, so obviously false,
not going to finish calculation.
No need to bother with 2nd inequality.