Question

Which of the following points lie in the solution set to the following system of inequalities?


`y < - 3x + 3 \\ y < x + 2`
A.(1,-5)
B.(1,5)
C.(5,1)
D.(-1,5)​

Answer 1

A. (1, -5)

Explanation:

Put the coordinates of the points to the each inequality, and check the inequality:

A. (1, -5)

y < -3x + 3

-5 < - 3(1) + 3

-5 < -3 + 3

-5 < 0 CORRECT

y < x + 2

-5 < 1 + 3

-5 < 3 CORRECT

B. (1, 5)

y < -3x + 3

5 < -3(1) + 3

5 < -3 + 3

5 < 0 FALSE

C. (5, 1)

y < -3x + 3

1 < -3(5) + 3

1 < -15 + 3

1 < -12 FALSE

D. (-1, 5)

y < -3x + 3

5 < -3(-1) + 3

5 < 3 + 3

5 < 6 CORRECT

y < x + 2

5 < -1 + 2

5 < 1 FALSE