Question

Solve the following pairs of equations:
$43x+67y=-24$ and $67x+43y=24$

Answer 1

Given,
$43x+67y=-24\dots \dots \left(i\right)$
$67x+43y=24\dots \dots \left(ii\right)$
on adding (i) and (ii), we get

$43x+67y+67x+43y=-24+24$

$\Rightarrow 110x+110y=0$

$\Rightarrow x+y=0\dots \dots \left(iii\right)$

and, on substracting (i) from (ii), we get

$67x+43y-(43x+67y)=24-(-24)$

$\Rightarrow 67x+43y-43x-67y=24+24$

$\Rightarrow 24x-24y=48$

$\Rightarrow x-y=2$

$\Rightarrow x=y+2$
on substituting the value of $x$ in (iii), we get

$(y+2)+y=0$

$\Rightarrow 2y=-2$

$\therefore y=-1$

On putting $y=-1$ in (iii), we get
$x+(-1)=0$

$\Rightarrow x=1$

$\therefore x=1,y=-1$