Solve the following systems of equations.
$x + y - z = 2, 2 x - y + 4 z = 1, - x + 6 y + z = 5$

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Solution

Given equations,
$x + y - z = 2$ $\to (1)$
$2 x - y + 4 z = 1$ $\to (2)$
$- x + 6 y + z = 5$ $\to (3)$
$(1) \times 4 + (2)$ $\Rightarrow$ $4 x + 4 y - 4 z + 2 x - y + 4 z = 9$
$6 x + 3 y = 9$
$2 x + y = 3$
$(1) + (3)$ $\Rightarrow$ $7 y = 7$
$y = 1$
$2 x + 1 = 3$
$x = 1$
$z = 0$ $9 ∵ x + y - z = 2)$
$∴$ $x = 1, y = 1, z = 0$ is solution of given equations.

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