Question

Solve for $x$ and $y$:
$11x+15y+23=0,7x-2y-20=0$

Answer 1

$11x+15y+23=\mathrm{0........}\left(1\right)$

$7x-2y-20=\mathrm{0........}\left(2\right)$

After multiplying equation $\left(1\right)$ by $2$ and equation $\left(2\right)$ by $15$ on addition we get,

$\begin{array}{cc}2\left(11x+15y+23\right)+15\left(7x-2y-20\right)& =0\\ 22x+30y+46+105x-30y-300& =0\\ 127x-254& =0\\ 127x& =254\\ x& =2\end{array}$

Substitute $x=2$ in equation $\left(1\right),$

$\begin{array}{cc}22+15y+23& =0\\ 15y+45& =0\\ 15y& =-45\\ y& =-3\end{array}$