Question

For each ordered pair (x, y), determine whether it is a solution to the inequality 5x+7y ≥ −3. ​

Answer 1

(-9,6) and (0,2) are the solutions to the inequality 5x+7y ≥ −3

Explanation:

let's plug in one by one

(-9,6)

5(-9)+7(6) ≥ −3

-45 + 42 ≥ −3

-3 ≥ −3 True

(0,2)

5(0)+7(2) ≥ −3

0 + 14 ≥ −3

14 ≥ −3 True

(3,-5)

5(3)+7(-5) ≥ −3

15 - 35 ≥ −3

-20 ≥ −3 False

(-4, -2)

5(-4)+7(-2) ≥ −3

-20 - 14 ≥ −3

-34 ≥ −3 False

Answer 2

Answer: From top to bottom, yes, yes, no, no

Explanation:

To see if these coordinate pairs are solutions, we will substitute them into the inequality 5x + 7y ≥ −3 and simplify. If the left side is greater than or equal to the right side, it's a solution.

✓ (-9, 6) ➜ 5x + 7y ≥ −3 ➜ 5(-9) + 7(6) ≥ −3 ➜ -3 ≥ −3, true

✓ (0, 2) ➜ 5x + 7y ≥ −3 ➜ 5(0) + 7(2) ≥ −3 ➜ 14 ≥ −3, true

✗ (3, -5) ➜ 5x + 7y ≥ −3 ➜ 5(3) + 7(-5) ≥ −3 ➜ -20 ≥ −3, false

✗ (-4, -2) ➜ 5x + 7y ≥ −3 ➜ 5(-4) + 7(-2) ≥ −3 ➜ -34 ≥ −3, false

I have also graphed this inequality and the given coordinate points, see attached. You will also find a visual example of the answer options attached too.