Question

Is (–4, 7) a solution to this system of inequalities?

x + 13y ≤ –16
20x − 9y ≤ –18
question



key idea
solution

Answer 1

Key idea: To test a point, substitute its coordinates into each inequality; the point must satisfy both.

Substitute (x,y) = (−4, 7):

1) x + 13y = −4 + 13(7) = −4 + 91 = 87.
87 ≤ −16? No.

2) 20x − 9y = 20(−4) − 9(7) = −80 − 63 = −143.
−143 ≤ −18? Yes.

Since the point fails the first inequality, (−4, 7) is not a solution to the system.