Is (4, –1) a solution to this system of inequalities?

Question

6x + 17y < 11
5x + 8y > 17

GPT-4o mini · Answer

To determine if the point $(4, -1)$ is a solution to the system of inequalities, we need to plug in the values $x = 4$ and $y = -1$ into both inequalities and see if they hold true. 1. For the first inequality: $$ 6x + 17y < 11 $$ Substituting $x$ and $y$: $$ 6(4) + 17(-1) < 11 $$ Calculate: $$ 24 - 17 < 11 $$ $$ 7 < 11 \quad \text{(True)} $$ 2. For the second inequality: $$ 5x + 8y > 17 $$ Substituting $x$ and $y$: $$ 5(4) + 8(-1) > 17 $$ Calculate: $$ 20 - 8 > 17 $$ $$ 12 > 17 \quad \text{(False)} $$ Since the first inequality is true, but the second inequality is false, the point $(4, -1)$ is **not** a solution to the system of inequalities.