Select all of the ordered pairs that are solutions to the following system of inequalities.
2x+2y≥7
y<3x–5
a. (3, 4)
b. (9, -3)
c. (2, -5)
d. (7, 0)
Substitute each ordered pair into the system of inequalities:
a. (3, 4)
2(3) + 2(4) = 6 + 8 = 14 ≥ 7 (true)
4 < 3(3) - 5 (true)
b. (9, -3)
2(9) + 2(-3) = 18 - 6 = 12 ≥ 7 (true)
-3 < 3(9) - 5 = 27 - 5 = 22 (true)
c. (2, -5)
2(2) + 2(-5) = 4 - 10 = -6 < 7 (false)
-5 < 3(2) - 5 = 6 - 5 = 1 (true)
d. (7, 0)
2(7) + 2(0) = 14 ≥ 7 (true)
0 < 3(7) - 5 = 21 - 5 = 16 (true)
Therefore, the ordered pairs that are solutions to the system of inequalities are:
b. (9, -3)
d. (7, 0)