MATH SOLVE

2 months ago

Q:
# Which of the following points lie in the solution set to the following system of inequalities? (1 point) y > β3x + 3 y > x + 2A. (2,-5)B. (-2,5)C. (2,5)D. (-2,-5)

Accepted Solution

A:

You can replace the values of x and y for each pair and check if they are solutions:

A. (2, - 5)

- 5 vs - 3(2) + 3

- 5 vs - 6 + 3

- 5 vs - 3 => - 5 < - 3, therefore this point does not meet the first inequality y > -3x + 3 and it is not a solution.

B. (-2,5)

5 vs - 2 + 2

5 vs 0 => 5 < 0, therefore this point does not meet the second inequality y > x + 2 and it is not a solution of the system.

C) (2,5)

5 vsΒ -3(2) + 3

5 vs - 6 + 3

5 vs - 3 => 5 > - 3, therefore the point meets the first inequality y > -3x + 3

5 vs 2 + 2

5 vs 5 => 5 > 4 , therefore the point meets the second inequality y > x + 2

Then, the point (2,5) meets both inequalities and it is a solution of the system.

Answer: option C(2,5)

A. (2, - 5)

- 5 vs - 3(2) + 3

- 5 vs - 6 + 3

- 5 vs - 3 => - 5 < - 3, therefore this point does not meet the first inequality y > -3x + 3 and it is not a solution.

B. (-2,5)

5 vs - 2 + 2

5 vs 0 => 5 < 0, therefore this point does not meet the second inequality y > x + 2 and it is not a solution of the system.

C) (2,5)

5 vsΒ -3(2) + 3

5 vs - 6 + 3

5 vs - 3 => 5 > - 3, therefore the point meets the first inequality y > -3x + 3

5 vs 2 + 2

5 vs 5 => 5 > 4 , therefore the point meets the second inequality y > x + 2

Then, the point (2,5) meets both inequalities and it is a solution of the system.

Answer: option C(2,5)