Is (2, 2) a solution to this system of inequalities?
5x + 2y ≥ 15
2x + y < 20
To check if the point (2, 2) is a solution to the system of inequalities, we need to substitute the values of x and y into each inequality and see if both inequalities are satisfied.
For the first inequality:
5x + 2y ≥ 15
Replacing x with 2 and y with 2:
5(2) + 2(2) ≥ 15
10 + 4 ≥ 15
14 ≥ 15
The inequality 14 ≥ 15 is false. Therefore, (2, 2) is not a solution to the first inequality.
For the second inequality:
2x + y < 20
Replacing x with 2 and y with 2:
2(2) + 2 < 20
4 + 2 < 20
6 < 20
The inequality 6 < 20 is true. Therefore, (2, 2) is a solution to the second inequality.
Since (2, 2) satisfies only one of the two inequalities, it is not a solution to the system of inequalities.