Is (4, -9) a solution to this system of inequalities?
y＜1/4x＋9
Y<= 1/2x+9
To determine whether (4, -9) is a solution to the system of inequalities, we substitute the values of x and y into each inequality and check if the inequalities hold true.
1) y < 1/4x + 9:
(-9) < (1/4)(4) + 9
-9 < 1 + 9
-9 < 10
The inequality is true.
2) y ≤ 1/2x + 9:
(-9) ≤ (1/2)(4) + 9
-9 ≤ 2 + 9
-9 ≤ 11
The inequality is also true.
Therefore, (4, -9) is a solution to the system of inequalities.