If 2x + 3y = 31 and 3x - y = 8, what is the value of the sum (x + y)?
Answer and explanation
Correct answer: C. 12
- Step 1: From equation 2: y = 3x - 8. Step 2. Substitute into equation 1: 2x + 3(3x - 8) = 31 => 2x + 9x - 24 = 31 => 11x = 55 => x = 5. Step 3. Find y: y = 3(5) - 8 = 15 - 8 = 7. Step 4. Sum x + y = 5 + 7 = 12. Answer: 12. Why not the others: x=4 and y=6 would yield 2(4)+3(6) = 26, not 31.
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