Which ordered pair is a solution for this system of inequalities?

2x + 3y > 1 and y < 5/4 x - 1

A. (3, 9)

B. (-4, 2)

C. (8, - 1)

D. (-2, - 5),

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.