Question

Y ≥ x + 1

x > -6
y ≤ 4

Which of the following points is a solution to this system of linear inequalities?

Answer 1

We can find a solution by checking if each given point satisfies all three inequalities:

(-5, 3): y = 3 ≥ -5 + 1 = -4 (satisfies the first inequality), -5 > -6 (satisfies the second inequality), 3 ≤ 4 (satisfies the third inequality). Therefore, (-5, 3) is a solution to the system of linear inequalities.

(-2, 6): y = 6 ≥ -2 + 1 = -1 (satisfies the first inequality), -2 > -6 (satisfies the second inequality), 6 ≤ 4 (does not satisfy the third inequality). Therefore, (-2, 6) is not a solution to the system of linear inequalities.

(0, -3): y = -3 ≤ 0 + 1 = 1 (does not satisfy the first inequality), 0 > -6 (satisfies the second inequality), -3 ≤ 4 (satisfies the third inequality). Therefore, (0, -3) is not a solution to the system of linear inequalities.

(4, 2): y = 2 ≥ 4 + 1 = 5 (does not satisfy the first inequality), 4 > -6 (satisfies the second inequality), 2 ≤ 4 (satisfies the third inequality). Therefore, (4, 2) is not a solution to the system of linear inequalities.

Therefore, the only point that is a solution to the system of linear inequalities is (-5, 3).xplanation: