Which of the following points are solutions to the system of inequalities shown below? Check all that apply. {:[y 1]:} A. (5,-6) B. (2,1) C. (1,4) D. (3,0) E. (0,6) F. (2,11)

Question

Which of the following points are solutions to the system of inequalities shown below? Check all that apply. {:[y <= -2x+6],[x > 1]:} A. (5,-6) B. (2,1) C. (1,4) D. (3,0) E. (0,6) F. (2,11)

Bytelearn · Accepted Answer

Check Point A Inequality: Check if point A (5, -6) satisfies the inequality y <= -2x + 6. Substitute x = 5 and y = -6 into the inequality y <= -2x + 6. -6 <= -2(5) + 6 -6 <= -10 + 6 -6 <= -4 Point A satisfies the first inequality: YesCheck Point A x: Check if point A (5, -6) satisfies the inequality x > 1. 5 > 1 Point A satisfies the second inequality: YesCheck Point B Inequality: Check if point B (2, 1) satisfies the inequality y <= -2x + 6. Substitute x = 2 and y = 1 into the inequality y <= -2x + 6. 1 <= -2(2) + 6 1 <= -4 + 6 1 <= 2 Point B satisfies the first inequality: YesCheck Point B x: Check if point B (2, 1) satisfies the inequality x > 1. 2 > 1 Point B satisfies the second inequality: YesCheck Point C Inequality: Check if point C (1, 4) satisfies the inequality y <= -2x + 6. Substitute x = 1 and y = 4 into the inequality y <= -2x + 6. 4 <= -2(1) + 6 4 <= -2 + 6 4 <= 4 Point C satisfies the first inequality: YesCheck Point C x: Check if point C (1, 4) satisfies the inequality x > 1. 1 > 1 Point C does not satisfy the second inequality: NoCheck Point D Inequality: Check if point D (3, 0) satisfies the inequality y <= -2x + 6. Substitute x = 3 and y = 0 into the inequality y <= -2x + 6. 0 <= -2(3) + 6 0 <= -6 + 6 0 <= 0 Point D satisfies the first inequality: YesCheck Point D x: Check if point D (3, 0) satisfies the inequality x > 1. 3 > 1 Point D satisfies the second inequality: YesCheck Point E Inequality: Check if point E (0, 6) satisfies the inequality y <= -2x + 6. Substitute x = 0 and y = 6 into the inequality y <= -2x + 6. 6 <= -2(0) + 6 6 <= 0 + 6 6 <= 6 Point E satisfies the first inequality: YesCheck Point E x: Check if point E (0, 6) satisfies the inequality x > 1. 0 > 1 Point E does not satisfy the second inequality: NoCheck Point F Inequality: Check if point F (2, 11) satisfies the inequality y <= -2x + 6. Substitute x = 2 and y = 11 into the inequality y <= -2x + 6. 11 <= -2(2) + 6 11 <= -4 + 6 11 <= 2 Point F does not satisfy the first inequality: No

Full solution

More problems from Is (x, y) a solution to the system of inequalities?

Related topics