Question

Is (4, 6) a solution to this system of inequalities?

y
<
1
2
x
+ 10

y
≥
1
4
x
− 7

Answer 1

Yes.

Plug (x,y) = (4,6) into each inequality:

1) y < (1/2)x + 10 → 6 < (1/2)(4) + 10 = 2 + 10 = 12, which is true.

2) y ≥ (1/4)x − 7 → 6 ≥ (1/4)(4) − 7 = 1 − 7 = −6, which is true.

Since both inequalities hold, (4,6) is a solution to the system.