Identify solution(s) to the system below. y−7x−5 y

Question

Identify solution(s) to the system below.

y>−7x−5
y<3x−15

Select all that apply.

BlackTom AI · Accepted Answer

We start by restating the system: y must be greater than -7x - 5 and also less than 3x - 15. In other words, points (x, y) must lie above the line y = -7x - 5 and below the line y = 3x - 15. Now, let’s test each given candidate point in turn to see if both inequalities hold. Option 1: (2, -12) - Check y > -7x - 5: compute -7x - 5 with x = 2 → -7(2) - 5 = -14 - 5 = -19. Is -12 > -19? Yes, this inequality holds. - Check y < 3x - 15: compute 3x - 15 with x = 2 → 3(2) - 15 = 6 - 15 = -9. Is -12 < -9? Yes, this inequality also holds. Conclusion for (2, -12): It satisfies both conditions, so it is a solution. Option 2: (5, -20) - Check y > -7x - 5: -7x - 5 with x = 5 → -7(5) - 5 = -35 - 5 = -40. Is -20 > -40? Yes, the first inequality is satisfied. - Check y < 3x - 15: 3x - 15 with x = 5 → 3(5) - 15 = 15 - 15 = 0. Is -20 < 0? Yes, the second inequality is satisfied. Conclusion for (5, -20): It also satisfies both conditions, so it is a solution. Option 3: (1, 9) - y > -7x - 5: -7(1) - 5 = -7 - 5 = -12. Is 9 > -12? Yes, the first inequality holds. - y < 3x - 15: 3(1) - 15 = 3 - 15 = -12. Is 9 < -12? No, this fails the second inequality. Conclusion for (1, 9): It does not satisfy all conditions, so it is not a solution. Option 4: (5, 0) - y > -7x - 5: -7(5) - 5 = -40. Is 0 > -40? Yes, the first inequality holds. - y < 3x - 15: 3(5) - 15 = 0. Is 0 < 0? No, it is not strictly less than 0 (it equals 0), so the second inequality fails. Conclusion for (5, 0): It does not satisfy all conditions, so it is not a solution. Summary: The points that satisfy both inequalities are (2, -12) and (5, -20). The other two options fail because they do not meet one of the two required inequalities.

ALGII141-027 Unit 3 Test

Identify solution(s) to the system below. y>−7x−5 y<3x−15 Select all that apply.

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