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CUET · MATHS · PYQ PAPER 2025

The value(s) of K, for which the system of linear equations 2x + y + x = 1, x + Ky - x = \(\frac{3}{2}\) and 3y - 5x = 9 does not possess a unique solution is

  1. A \(K=\frac{7}{5}\)
  2. B \(K=-\frac{7}{5}\)
  3. C \(K \in R-\left\{\frac{7}{5}\right\}\)
  4. D \(K \in R-\left\{-\frac{7}{5}\right\}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(K=\frac{7}{5}\)

Step-by-step Solution

Detailed explanation

\(\begin{vmatrix} 2 & 1 & 1 \\ 1 & K & -1 \\ 0 & 3 & -5 \end{vmatrix} = 0\) \(2(-5K - (-3)) - 1(-5 - 0) + 1(3 - 0) = 0\) \(2(-5K + 3) + 5 + 3 = 0\) \(-10K + 6 + 8 = 0\) \(-10K + 14 = 0\) \(-10K = -14\) \(K = \frac{14}{10}\) \(K = \frac{7}{5}\)