Answer:
Question 1
Ordered pair (2, -3) satisfies y ≥ x - 5 but does not satisfy y ≤ 2x-8
Question 2
Ordered pair (0,4) does satisfy both inequalities:
y ≤ -x + 4 and y ≥ 5x - 3
Explanation:
Question 1
The ordered pair is (2, -3); therefore x = 2, y = -3
Plug these values into the left and right side of each inequality and see if these values satisfy the inequality
For y ≥ x - 5
LHS = -3, RHS = 2 - 5 = -3
Is -3 ≥ -3? Of course; in fact it is = and it only need to satisfy either = or >
For y ≤ 2x-8
LHS = -3, RHS = 2(2) - 8 = 4 - 8 = -4
Is -3 ≤ -4? NO. -3 is greater than -4
(remember in negative numbers -4 lies further to the left than -3 on the number line so -4 is less than -3)
Question 2
Given ordered pair is (0,4)
For y ≤ -x + 4
LHS = 4, RHS = -0 + 4 = 4
Is 4 ≤ 4? YES
For y ≥ 5x -3
LHS = 4, RHS = 5(0) -3 = 0 - 3 = -3
Is 4 ≥ -3? Of course. All positive numbers are greater than negative numbers