Question

Which of the following points lie in the solution set to the following system of inequalities?

y ≤ x − 5
y ≥ −x − 4

A. (-5,2)
B. (5,-2)
C. (-5,-2)
D. (5,2)

Answer 1

A. NOT

(-5, 2) → x = -5, y = 2

y ≤ x - 5 → 2 ≤ -5 - 5 → 2 ≤ -10 FALSE

B. YES

(5, -2) → x = 5, y = -2

y ≤ x - 5 → -2 ≤ 5 - 5 → -2 ≤ 0 TRUE

y ≥ -x - 4 → -2 ≥ -5 - 4 → -2 ≥ -9 TRUE

C. NOT

(-5, -2) → x = -5, y = -2

y ≤ x - 5 → -2 ≤ -5 - 5 → -2 ≤ -10 FALSE

D. NOT

(5, 2) → x = 5, y = 2

y ≤ x - 5 → 2 ≤ 5 - 5 → 2 ≤ 0 FALSE