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

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Solution

Given equations
$y + x - 1 = 0$
$| y | - x - 1 = 0$
If $y \geq 0$
$x + y = 1$
$y - x = 1$
$y = 1, x = 0$
If $y < 0$
$x + y = 1$
$- x - y = 1$
No solution.
$∴$ $x = 0, y = 1$ is solution of given equation.

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