Question

Solve : $3x+2y=4$

$8x+5y=9$

Answer 1

We have

$3x+2y=4\dots \dots \left(i\right)$

$8x+5y=9\dots \dots \left(ii\right)$

On multiplying eq.(i) by 5 and eq.(ii) by 2, we get

$15x+10y=20\dots \dots \left(iii\right)$

$16x+10y=18\dots \dots \left(iv\right)$

On subtracting eq.(iv) from eq.(iii), we have

$15x+10y-(16x+10y)=20-18$

$\Rightarrow -x=2$

$\Rightarrow x=-2$

On putting $x=-2$ in eq.(i), we get

$3\times (-2)+2y=4$

$\Rightarrow 2y=4+6$

$\Rightarrow y=5$

Hence, $x=-2$ and $y=5$