Question

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

Answer 1

Given equations,

$y-2x+1=0$

$y-1\times 1-1=0$

If $x\ge 0,$ $y-2x=-1$

$y-x=1$

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

$x=2$

$y=3$

If $x<0$, $y-2x=-1$

$y+x=1$

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

$3x=2$

$x=\frac{2}{3}$ but $x\ne \frac{2}{3}(\because c<0)$

$y=1-x=\frac{1}{3}$ (not a solution)

$\therefore x=2,y=3$ is solution of given equations.