Question

Solve the following pair of linear equations by elimination method.
$4x+19y+13=0$
$13x-23y+19=0$

Answer 1

$4x+19y+13=0$

$13x-23y+19=0$

By elimination method,

$13(4x+19y+13)=0$

$4(13x-23y+19)=0$

$\Rightarrow 52x+247y+169=0$

$52x-92y+76=0$

- + -

_________________

$339y+93=0$

$y=\frac{-93}{339}=\frac{-31}{113}$

$4x+19\left(\frac{-31}{113}\right)+13=0$

$4x=\frac{539}{113}-13=\frac{880}{113}\Rightarrow x=\frac{-220}{113}$

$y=\frac{-31}{113}$