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) (2,-5)
c) (9,-3)
d) (7,0)
The solutions to the system of inequalities are the ordered pairs that satisfy both inequalities when plugged into them.
Let's check each ordered pair:
a) (3,4)
2(3) + 2(4) = 6 + 8 = 14 (Doesn't satisfy 2x + 2y ≥ 7, so not a solution)
4 < 3(3) - 5
4 < 9 - 5
4 < 4 (Doesn't satisfy y < 3x - 5, so not a solution)
b) (2,-5)
2(2) + 2(-5) = 4 - 10 = -6 (Doesn't satisfy 2x + 2y ≥ 7, so not a solution)
-5 < 3(2) - 5
-5 < 6 - 5
-5 < 1 (Satisfies y < 3x - 5, so possible solution)
c) (9,-3)
2(9) + 2(-3) = 18 - 6 = 12 (Doesn't satisfy 2x + 2y ≥ 7, so not a solution)
-3 < 3(9) - 5
-3 < 27 - 5
-3 < 22 (Satisfies y < 3x - 5, so possible solution)
d) (7,0)
2(7) + 2(0) = 14 (Satisfies 2x + 2y ≥ 7)
0 < 3(7) - 5
0 < 21 - 5
0 < 16 (Satisfies y < 3x - 5)
Therefore, the solutions to the system of inequalities are:
b) (2,-5)
d) (7,0)