Is (8, 8) a solution to this system of inequalities?

Question

11x + 18y ≥ 4
15x + y < –5

Answer 1

To determine if the point (8, 8) is a solution to the system of inequalities, we will substitute \( x = 8 \) and \( y = 8 \) into each inequality.

1. For the first inequality:
   \( 11x + 18y ≥ 4 \)
   Substituting the values:
   \( 11(8) + 18(8) ≥ 4 \)
   \( 88 + 144 ≥ 4 \)
   \( 232 ≥ 4 \)
   This inequality is true.

2. For the second inequality:
   \( 15x + y < -5 \)
   Substituting the values:
   \( 15(8) + 8 < -5 \)
   \( 120 + 8 < -5 \)
   \( 128 < -5 \)
   This inequality is false.

Since (8, 8) satisfies the first inequality but not the second, it is not a solution to the system of inequalities.