Final answer:
The correct answer to the system of inequalities 2y + 7 > 13 or -3y - 2 > 10, is B) y > 3, because when each inequality is solved for y, the first inequality reduces to y > 3 and the second reduces to y < -4.
Step-by-step explanation:
To solve the system of inequalities 2y + 7 > 13 or -3y - 2 > 10, we need to isolate the variable y in each inequality.
Starting with the first inequality 2y + 7 > 13:
- Subtract 7 from both sides: 2y > 6.
- Divide both sides by 2: y > 3.
Now, looking at the second inequality -3y - 2 > 10:
- Add 2 to both sides: -3y > 12.
- Divide both sides by -3, and remember to flip the inequality sign when dividing by a negative number: y < -4.
The solution is the set of all y such that y > 3 or y < -4. Comparing with the options provided:
- A) y < 3 (Incorrect)
- B) y > 3 (Correct)
- C) y < -5 (Not the exact solution, but it is contained within y < -4)
- D) y > -5 (Incorrect, because this does not include all values greater than 3)
Therefore, the correct answer is B) y > 3.