The simultaneous equation, $y = x + 2 | x |$ & $y = 4 + x - | x |$ have the solution set given by

(\frac{4}{3}, \frac{8}{3})

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(4, \frac{4}{3})

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(\frac{4}{3}, \frac{4}{3})

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(\frac{4}{3}, 4)

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Solution

The correct option is B $(\frac{4}{3}, 4)$
if $x < 0$ then ;
$y = - x, y = 4 + 2 x ⟹ x = \frac{- 4}{3}, y = \frac{4}{3} ⟹ (\frac{- 4}{3}, \frac{4}{3})$
if $x \geq 0$ then ;
$y = 3 x, y = 4 ⟹ x = \frac{4}{3} ⟹ (\frac{4}{3}, 4)$

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