GATE CS 2026 Set 2 — Question 31
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+1 / -0MediumSystem of Linear EquationsLinear AlgebraEngineering Mathematics
Engineering Mathematics → Linear Algebra → System of Linear Equations
Last updated
Question
Consider the system of linear equations given below.Suppose the values of and are chosen such that the system of linear equations produce multiple solutions. Then the product of and is __________. (answer in integer)
Correct answer
24 to 24
Solution
For a system of linear equations to have multiple (infinite) solutions, the lines must be coincident. The condition for the system and to have infinite solutions is:Substituting the given values:From the first part:Case 1: If , then:Product .Case 2: If , then:Product .In both cases, the product of and is 24.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Linear Algebra
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…