Select all of the ordered pairs that are solutions to the following system of inequalities.
2x+2y≥7
y<3x–5
3,4
2,-5
9,-3
7,0
Let's test each ordered pair in the system of inequalities:
1. (3,4)
2(3) + 2(4) = 6 + 8 = 14 ≥ 7
4 < 3(3) - 5 => 4 < 4
This pair does not satisfy the second inequality.
2. (2,-5)
2(2) + 2(-5) = 4 - 10 = -6 < 7
-5 < 3(2) - 5 => -5 < 6
This pair satisfies both inequalities.
3. (9,-3)
2(9) + 2(-3) = 18 - 6 = 12 ≥ 7
-3 < 3(9) - 5 => -3 < 22
This pair satisfies both inequalities.
4. (7,0)
2(7) + 2(0) = 14 ≥ 7
0 < 3(7) - 5 => 0 < 16
This pair satisfies both inequalities.
Therefore, the solutions are:
(2,-5)
(9,-3)
(7,0)