Solve the following system of equation:
$| x - 1 | + y = 0, 2 x - y = 1$

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Solution

Given equations,
$| x - 1 | + y = 0$
$2 x - y = 1$
$\Rightarrow$ $2 x + | x - 1 | = 1 (∵ y = - | x - 1 |)$
If $x \geq 1$ ,
$2 x + (x - 1) = 1$
$x = \frac{2}{3}$
But $x > 1$
$x \neq \frac{2}{3}$
If $x < 1$
$2 x + 1 - x = 1$
$x = 0$
$y = - 1 (∵ y = - | x - 1 |)$
$x = 0, y = - 1$ is possible solution of given equations.

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