Question

Solve the following systems of equations.
$|x-y|=12y-11,y+1=2x$

Answer 1

Let the given equation be,

$(x-y)=12y-11$

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

Let, $x-y=12y-11$ (equation $2$)

$x-y+12y-11=0$ (equation $3$)

On solving equation $1$ and $2$

i.e, $2x-y-1=0$

and $2x-26y+22=0$

After solving, $25y-23=0$

So, $y=\frac{23}{25}$

$\Rightarrow x=\frac{24}{25}$

On solving equation $1$ and $3$

i.e, $x+11y-11=0$

and $x-\frac{y}{2}-\frac{1}{2}=0$

After solving, $\frac{23y}{2}-\frac{21}{2}=0$

So, $y=\frac{21}{23}$

$\Rightarrow x=\frac{22}{23}$

This solution is not accepted as we assumed $y>x$

Solution is $(x,y)=(\frac{24}{25},\frac{23}{25})$