Allied & ICAR Exam Bank • ALLIED_0776 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Systems of linear equations

Question Statement:

The system of linear equations $x + 2y = 5$ and $3x + k y = 15$ has infinitely many solutions. The value of $k$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

For infinitely many solutions, equations must be proportional: $3/1 = k/2 = 15/5 = 3 \implies k = 6$.
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