Consider the following systme of euqtions:
y >_ 2x -6
y < 5x + 2
Describe ho you could determine wheater((5, 2) is a solution to the system of inequalitie
To determine whether (5, 2) is a solution to the system of inequalities, we need to substitute the values of x = 5 and y = 2 into the two inequalities and check if both are satisfied.
1. Substitute x = 5 and y = 2 into y ≥ 2x - 6:
2 ≥ 2(5) - 6
2 ≥ 10 - 6
2 ≥ 4
Since 2 is greater than or equal to 4, this inequality is not satisfied.
2. Substitute x = 5 and y = 2 into y < 5x + 2:
2 < 5(5) + 2
2 < 25 + 2
2 < 27
Since 2 is less than 27, this inequality is satisfied.
Therefore, (5, 2) is not a solution to the system of inequalities because it does not satisfy the first inequality.