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GATE CSE 2026 Session 2 Q31: Product ab for a 2×2 linear system with infinitely many solutions

Question

Consider the system of linear equations given below.

ax+y=bax + y = b 16x+ay=2416x + ay = 24

Suppose the values of aa and bb are chosen such that the system of linear equations produce multiple solutions. Then the product of aa and bb is __________. (answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 24 (official GATE 2026 final answer key)

Concept used: Two equations have infinitely many solutions when they are proportional.

First step: Set a16=1a=b24\frac{a}{16} = \frac{1}{a} = \frac{b}{24} and solve for aa and bb.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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