AP EAMCET · Maths · Determinants
If the system of simultaneous linear equations \(3 x-4 y+k z+13=0, x+2 y-z-9=0\) and \(k x-y+3 z+7=0\) has a unique solution \(x=\alpha, y=\beta, z=\gamma\) for \(k \neq m\) and \(2 \beta-\gamma=8\), then \(\alpha+m=\)
- A 10
- B 8
- C -2
- D 9
Answer & Solution
Correct Answer
(C) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }\left|\begin{array}{ccc}3 & -4 & k \\ 1 & 2 & -1 \\ k & -1 & 3\end{array}\right| \neq 0 \\ & \Rightarrow \quad 3(6-1)+4(3+k)+k(-1-2 k) \neq 0 \\ & \Rightarrow 15+12+4 k-k-2 k^2 \neq 0 \\ & \Rightarrow \quad 2 k^2-3 k-27 \neq 0 \Rightarrow 2 k^2-9 k+6…
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