If $| x + 2 | + y = 5$ and $x - | y | = 1$ , then find the value of $x + y$ .

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Solution

$| y | = x - 1$

since $| y |$ is always positive

$x - 1$ will always be a positive number

That means x is always greater than equal to 1

so now the equations become

$x + 2 + y = 5$ ...(1)

$x - y = 1$ ...(2)

solving (1) and (2) we get,

$x = 2$ and $y = 1$

$\Rightarrow x + y = 2 + 1 = 3$

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