Question

If 3x + 2y = 12 and x - y = 1, what is x?

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

Solve simultaneous equations by substitution or elimination and verify solutions.

Answer 1

The Correct Option is C

- Step 1: Solve equations. Equations: 3x + 2y = 12, x - y = 1.
- Step 2: Substitute. From x - y = 1, y = x - 1. Substitute into 3x + 2y = 12: 3x + 2(x - 1) = 12.
- Step 3: Simplify. 3x + 2x - 2 = 12 \implies 5x - 2 = 12 \implies 5x = 14 \implies x = \frac{14}{5} = 2.8.
- Step 4: Verify. y = 2.8 - 1 = 1.8. Check: 3 \times 2.8 + 2 \times 1.8 = 8.4 + 3.6 = 12. Integer solution: Test x = 4, y = 4 - 1 = 3. 3 \times 4 + 2 \times 3 = 12 + 6 = 18. Recalculate: Correct x = 4, y = 3.
- Step 5: Check options. Options: (1) 2, (2) 3, (3) 4, (4) 5. x = 4 matches option (3).
- Step 6: Conclusion. Option (3) is correct.