Question

Solve the following systems of equations.
$|x|+2|y|=3,5y+7x=2$

Answer 1

Given,

$|x|+2|y|=3$ (equation $1$)

$5y+7x=2$ (equation $2$)

From equation $1$,

for $x>0,y>0$

$x+2y=3$

$7x+5y=2$

for $x<0,y>0$

$-x+2y=3$

$\Rightarrow x-2y+3=0$

for $x<0,y<0$

$x+2y+3=0$

for $x>0,y<0$

$x-2y=3$

Actually, the graph of above obtained looks like above figure

But as we restricted our domain accordingly as $x<0$ (or) $x>0$ and $y<0$ (or) $y>0$

The actual solutions are the point of intersection of lines at $B$ and $D$

Solving $7x+5y=2$ (equation $3$)

and $x-2y+3=0$

$\Rightarrow 7x-14y+21=0$ (equation $4$)

from equation $4$ and $5$

$19y=23$

$y=\frac{23}{19},x=\frac{-77}{19}$

Solving $x-2y=3$ and $7x+5y=2$

$\Rightarrow y=-1x=1$

Solutions are $(1,-1)$ and $(\frac{-77}{19},\frac{23}{19})$