Question

Is (10, 4) a solution to this system of inequalities?

y
<
1
10
x
+ 10

y
≥
–1
5
x
+ 6

Answer 1

Yes.

Substitute x = 10, y = 4:

1) y < (1/10)x + 10 → 4 < (1/10)(10) + 10 = 1 + 10 = 11 — true.

2) y ≥ −(1/5)x + 6 → 4 ≥ −(1/5)(10) + 6 = −2 + 6 = 4 — true (equality allowed).

Since both inequalities hold, (10, 4) is a solution.