The number of solutions of the system of equations $2 x + y - z, x - 3 y + 2 z = 1$ and $x + 4 y - 3 z = 5$ is?

3

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2

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1

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0

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Solution

The correct option is D $0$
Given equations are $2 x + y - z$ , $x - 3 y + 2 z = 1$ and $x + 4 y - 3 z = 5$
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & - 1 1 & - 3 & 2 1 & 4 & - 3 \end{matrix} ∣ ∣ ∣ ∣$
$= 2 (9 - 8) - 1 (- 3 - 2) - 1 (4 + 3)$
$= 7 - 7 = 0$ .
Hence, the number of solutions is zero.

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