How do you solve 11x + 3y + 7 = 0 , 2x +5y - 21 = 0?

Sep 15, 2015

I found:
$x = - 2$
$y = 5$

Explanation:

You can try by multiplying the first equation by $- 2$ and the second by $11$ and then add together (in columns) the two equations to get:

$\left\{\begin{matrix}\left(\textcolor{red}{- 2}\right) \times 11 x + 3 y + 7 = 0 \\ \left(\textcolor{red}{11}\right) \times 2 x + 5 y - 21 = 0\end{matrix}\right.$

$\left\{\begin{matrix}- 22 x - 6 y - 14 = 0 \\ 22 x + 55 y - 231 = 0\end{matrix}\right.$ add them:

$0 + 49 y - 245 = 0$
$y = \frac{245}{49} = 5$

substitute this value into the first equation:
$11 x + 15 + 7 = 0$
$11 x = - 22$
$x = - \frac{22}{11} = - 2$