SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · General Intelligence and Reasoning · Question 15 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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If x+2y=14 and x−y=5, find x.

(a)6
(b)4
(c)8
(d)10

Answer

Why

Correct — C. Rule: subtract one equation from the other so that x cancels.

(x + 2y) − (x − y) = 14 − 5
3y = 9
y = 9 ÷ 3 = 3

Put y = 3 into x − y = 5:
x = 5 + 3 = 8 → option (c)

Check in the other equation: 8 + 2 × 3 = 14 ✓

Why the others are wrong

(a)
6 — x = 6 forces y = 1 from x − y = 5, and then x + 2y = 6 + 2 = 8, not 14.
(b)
4 — x = 4 forces y = −1 from x − y = 5, and then x + 2y = 4 − 2 = 2, not 14.
(d)
10 — x = 10 forces y = 5 from x − y = 5, and then x + 2y = 10 + 10 = 20, not 14.

Concept

These two equations have exactly one solution, because their x : y coefficient ratios differ: 1 : 2 against 1 : −1.

Elimination removes one letter by adding or subtracting the equations. Here both carry a single x, so subtracting them cancels x at once and leaves 3y = 9.

With y known, either equation gives x. Putting both values back into the other equation is the check that catches a sign slip.

Testing the options is just as fast here: each x gives y from x − y = 5, and x = 8 is the value that also satisfies x + 2y = 14.

Key facts

Subtracting x − y = 5 from x + 2y = 14 gives 3y = 9.
The solution is x = 8, y = 3.
A pair solves the system only if it satisfies both equations.

Study next

Elimination when one equation must first be multiplied to match coefficientsThree equations in x, y and z solved one unknown at a timeConditions for no solution or infinitely many solutions

Common traps

Adding the equations instead of subtracting, which gives 2x + y = 19 and removes neither letter.
Subtracting y's terms with the wrong sign: 2y − (−y) is 3y, not y.

Removing one unknown at a time also decides 11 Sep 2024, 09:00, Quant Q.16, where x + 2z = 3 and 3x − 5z = −13 give z = 2 and x = −1 before y is found.

Related PYQs

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