Question

Help me please if you can A.(0, 3)B. (-1, 5)C.(1, 1.5)

Answer 1

A. (0, 3)

C. (1, 1.5)

Step-by-step explanation:

A point is a solution to the system if it satisfies both inequalities.

So for each option, we get:

Replacing (x, y) = (0, 3)

y ≥ -2x + 3

3 ≥ -2(0) + 3

3 ≥ 3

y ≤ -x² - x + 4

3 ≤ -0² - 0 + 4

3 ≤ 4

Since both inequalities are satisfied, (0, 3) is a solution.

For (x, y) = (-1, 5)

y ≥ -2x + 3

5 ≥ -2(-1) + 3

5 ≥ 2 + 3

5 ≥ 5

y ≤ -x² - x + 4

5 ≤ -(-1)² - (-1) + 4

5 ≤ -1 + 1 + 4

5 ≤ 4

Since 5 is not lower than 4, (-1, 5) is not a solution

For (x, y) = (1, 1.5)

y ≥ -2x + 3

1.5 ≥ -2(1) + 3

1.5 ≥ -2 + 3

1.5 ≥ 1

y ≤ -x² - x + 4

1.5 ≤ -(1)² - (1) + 4

1.5 ≤ -1 - 1 + 4

1.5 ≤ 2

Since both inequalities are satisfied, (1, 1.5) is a solution.

Therefore, the answers are

A. (0, 3)

C. (1, 1.5)