Question

Solve the following systems of equations.
$x+2y-6=0,|x-3|-y=0$

Answer 1

Given equations,

$x+2y-6=0$

$|x-3|-y=0$

$y=|x-3|$

$x+2|x-3|-6=0$

If $x\ge 0$,

$x+2x-6-6=0$

$x=4$

$y=|x-3|=1$

If $x\le 3$,

$x-2x+6-6=0$

$x=0$

$y=|x-3|=3$

$\therefore (x=4,y=1)$ and $(x=0,y=3)$ is possible solution of given equations.