Question

Which point would be a solution to the system of linear inequalities shown below?

y ≥ 1/4 x+4 y ≤ -2x-7
O (-4,9)
O (8, 10)
O (4,0)
O (-8,8)

Answer 1

To determine which point is a solution to the given system of linear inequalities, substitute the values of x and y into the inequalities and check if either inequality holds. The point (-8, 8) is found to satisfy both inequalities and is a solution to the system.

Step-by-step explanation:

To determine which point is a solution to the given system of linear inequalities, we substitute the values of x and y into the inequalities and check if the inequalities are satisfied.

1. For the first inequality, y ≥ 1/4x + 4, we substitute the x and y values of each point and check if the inequality holds.
2. For the second inequality, y ≤ -2x - 7, we again substitute the x and y values of each point and check if the inequality holds.
3. Based on our calculations, we find that the point (-8, 8) satisfies both inequalities and is therefore a solution to the system of linear inequalities.