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GATE 2025 BT – Question 34

Engineering Mathematics · Linear Algebra: Matrices and determinants, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Numerical answer

The value of $k$, for which the linear equations $2x + 3y = 6$ and $4x + 6y = 3k$ have at least one solution, is _____________. (Answer in integer)

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Correct answer: 4

Explanation

Doubling the first equation gives $4x + 6y = 12$. The two equations are consistent (the lines coincide) only when $3k = 12$, so $k = 4$. Otherwise the lines are parallel and have no solution.