Q47 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

The system of simultaneous linear equations $x-2 y+3 z=4,3 x+y-2 z=7,2 x+3 y+z=6$ has

  • A
    infinitely many solutions
  • B
    no solution
  • C
    unique solution having $z=2$
  • Correct answer
    D
    unique solution having $z=\frac{1}{2}$

Solution

$D=\left|\begin{array}{ccc}1 & -2 & 3 \\ 3 & 1 & -2 \\ 2 & 3 & 1\end{array}\right|=42$ $D \neq 0$ therefore unique solution $\begin{aligned} & D_2=\left|\begin{array}{ccc} 1 & -2 & 4 \\ 3 & 1 & 7 \\ 2 & 3 & 6 \end{array}\right|=21 \\ & z=\frac{D_2}{D}=\frac{21}{42}=\frac{1}{2} . \end{aligned}$

Hence, the correct answer is option: 'D'.

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