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) and c) are ruled out because if x = -5..

y <= x - 5
y <= (-5) - 5
y <= -10

but the y coordinate in a) is 2, and in c.) is -2. both of which are greater than -10

d is ruled out for the same reason

if x = 5
y <= x - 5
y <= 5 - 5
y <= 0

but d.) has a y component of 2, which is greater than 0

that leaves b.)