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TS EAMCET · Maths · Determinants

If \(x=\alpha, y=\beta, z=\gamma\) is the unique solution of the system of linear equations \(2 x-3 y+5 z=12,5 x+2 y+3 z=11\) and \(x+2 y-3 z=-3\) then \(2 \alpha+5 \beta+3 \gamma=\)

  1. A 10
  2. B 11
  3. C 3
  4. D 2
Verified Solution

Answer & Solution

Correct Answer

(D) 2

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text 2 x-3 y+5 z=12 \\ & 5 x+2 y+3 z=11 \\ & x+2 y-3 z=-3 \\ & D=\left|\begin{array}{ccc}2 & -3 & 5 \\ 5 & 2 & 3 \\ 1 & 2 & -3\end{array}\right| \\ & =2(-6-6)+3(-15-3)+5(10-2) \\ & =-24-54+40=-38 \text {. } \\ & D_1=\left|\begin{array}{ccc}12 & -3 & 5 \\ 11 &…