Question

Which ordered pair makes both inequalities y≥-2x 3 y≤x-2 true?

1) (0,0)
2) (0,-1)
3) Cannot be determined
4) None of the above

Answer 1

The ordered pair that makes both inequalities y≥-2x+3 and y≤x-2 true is (0, 0). The inequalities are satisfied by this pair since both 0≥3 and 0≤-2 hold true.

Step-by-step explanation:

The question asks to determine which ordered pair makes both inequalities y≥-2x+3 and y≤x-2 true. To find a solution, we plug the x and y values from each of the ordered pairs into both inequalities and see if they both hold true.

• For (0, 0): We check if 0≥(-2*0)+3, which simplifies to 0≥3 and is true; and if 0≤0-2, which simplifies to 0≤-2 and is also true. Thus, the ordered pair (0, 0) satisfies both inequalities.
• For (0, -1): We check if -1≥(-2*0)+3, which simplifies to -1≥3 and is false; and if -1≤0-2, which simplifies to -1≤-2 and is false. Therefore, the ordered pair (0, -1) does not satisfy either inequality.

Hence, the ordered pair that makes both inequalities true is (0, 0).