Solve by Cramer's rule
$x + y + z = 6$
$x - y + z = 2$
$3 x + 2 y - 4 z = - 5$ . The value of x is

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Solution

$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 1 & - 1 & 1 3 & 2 & - 4 \end{matrix} ∣ ∣ ∣ ∣ = 1 (4 - 2) - 1 (- 4 - 3) + 1 (3 + 2) = 14$
$Δ_{x} = ∣ ∣ ∣ ∣ \begin{matrix} 6 & 1 & 1 2 & - 1 & 1 - 5 & 2 & - 4 \end{matrix} ∣ ∣ ∣ ∣ = 6 (4 - 2) - 1 (- 8 + 5) + 1 (4 - 5) = 14$
Hence by cramer rule,
$x = \frac{Δ_{x}}{Δ} = 1$

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