If \(x + 2y = 14\) and \(x - y = 5\) , find x.

Question

If \(x + 2y = 14\) and \(x - y = 5\) , find x.

1. A. 6
2. B. 4
3. C. 8 (Correct answer)
4. D. 10

Correct Answer

Option C — 8

Detailed Solution & Explanation

The correct answer is 8.

Key Points

• From x + 2y = 14 and x − y = 5, subtract the second from the first: (x + 2y) − (x − y) = 14 − 5.
• That gives 3y = 9, so y = 3.
• Substituting back: x = 5 + y = 8.
• Eliminate the variable the question does *not* ask about — here subtracting kills x immediately and gives y in one step.
• Substituting back into the untouched equation is the safest check: 8 + 2(3) = 14 ✓ and 8 − 3 = 5 ✓.
• With two linear equations, choose between elimination and substitution by looking at the coefficients — here the matching x terms make elimination a single subtraction.

Additional Information

• Elimination suits equations sharing a variable with matching coefficients; substitution suits an equation already solved for one variable.
• Always substitute the answer back into the equation you did *not* use, which catches sign errors that otherwise pass unnoticed.
• Simultaneous equations appear in the reasoning section as well as in quant, usually disguised as an age, ratio or coin problem.

प्रश्न (हिन्दी में)

यदि \(x + 2y = 14\) और \(x - y = 5\) है, तो x ज्ञात कीजिए।

1. A. 6
2. B. 4
3. C. 8
4. D. 10