Is (2, 8) a solution to this system of inequalities?
y ≥ 7х + 2
y 2 x+ 6
To determine if (2, 8) is a solution to the system of inequalities, we need to substitute the given values into both inequalities and check if the results are true.
1) y ≥ 7x + 2:
Substituting x = 2 and y = 8 into the inequality, we get:
8 ≥ 7(2) + 2
8 ≥ 14 + 2
8 ≥ 16
This statement is false since 8 is not greater than or equal to 16.
2) y ≤ 2x + 6:
Substituting x = 2 and y = 8 into the inequality, we get:
8 ≤ 2(2) + 6
8 ≤ 4 + 6
8 ≤ 10
This statement is true since 8 is less than or equal to 10.
Therefore, (2, 8) is not a solution to the given system of inequalities.