Question

Is (–1, –7) a solution to this system of inequalities?

8x − 3y ≤ 13
13x − 8y > –5
question



key idea
solution

Answer 1

Key idea: To test whether a point solves a system of inequalities, substitute the coordinates into each inequality and check whether each one is true.

Solution:
1) For 8x − 3y ≤ 13, substitute (x,y) = (−1, −7):
8(−1) − 3(−7) = −8 + 21 = 13, and 13 ≤ 13 is true.

2) For 13x − 8y > −5, substitute:
13(−1) − 8(−7) = −13 + 56 = 43, and 43 > −5 is true.

Both inequalities are satisfied, so (−1, −7) is a solution to the system.