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GATE CSE 2025 Session 1 Q23: Values of k for which x + ky = 1, kx + y = −1 is solvable

Question

Consider the given system of linear equations for variables xx and yy, where kk is a real-valued constant. Which of the following option(s) is/are CORRECT?

x+ky=1kx+y=−1\begin{aligned} x + ky &= 1 \\ kx + y &= -1 \end{aligned}

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: A, D (official GATE 2025 final answer key)

Concept used: A 2×2 system has a unique solution iff the determinant is non-zero; otherwise check consistency.

First step: The determinant is 1−k21 - k^2, so only k=1k = 1 and k=−1k = -1 need checking; substitute each into both equations.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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