Solve the equations by reduction method; $2 x - 4 y + 3 z = 1, x - 2 y + 4 z = 3, 3 x - y + 5 z = 2$

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Solution

$2 x - 4 y + 3 = 1 x - 2 y + 4 z = 3; 3 x - y + 5 z = 2$
Let $z = k$
$\Rightarrow 2 x - 4 y = 1 - 3 z \to (1) x - 2 y = 3 - 4 z \to (2)$
and $3 x - y = 2 - 5 z \to (3) 2 \times 3 \to 3 3 x - 6 y = 9 - 12 z 3 x - y = 2 - 5 z - + - + - - - - - - - - - - 5 y = 7 - 7 z \Rightarrow y = (7 z - 7) 5 = \frac{7}{5} (z - 1)$
also $3 x - y = 2 - 5 z \Rightarrow 3 x - \frac{7}{[} 5] (z - 1) = 2 - 5 z \Rightarrow 3 x = \frac{(2 - 5 z) 5}{+} 7 (z - 1) 5 3 x = \frac{10 - 25 z + 7 x - 7}{5} \Rightarrow x \frac{3 - 18 z}{5}$ and $y = \frac{7}{5} (z - 1)$

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