CUET · MATHS · PYQ PAPER 2025
The value of \(k\) for which the system of equations
\(\begin{array}{l}x+y+z=1 \\x-k y+z=1\end{array}\)
\(x-y+z=1\)
has more than one solution is :
- A only 1
- B only -1
- C 1 and -1 only
- D any real number
Answer & Solution
Correct Answer
(D) any real number
Step-by-step Solution
Detailed explanation
\((x+y+z)-(x-y+z) = 1-1 \Rightarrow 2y=0 \Rightarrow y=0\) Substitute \(y=0\) into \(x+y+z=1 \Rightarrow x+0+z=1 \Rightarrow x+z=1\) Substitute \(y=0\) into \(x-ky+z=1 \Rightarrow x-k(0)+z=1 \Rightarrow x+z=1\) The system reduces to \(y=0\) and \(x+z=1\), which has infinitely…
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