# How do you solve the following system?: 2x +5y =-1 , -5x -3y = 2

Apr 29, 2017

$x = - \frac{7}{19} \text{ }$ and $\text{ } y = - \frac{1}{19}$

#### Explanation:

$2 x + 5 y = - 1 \text{ " stackrel (xx 3) rarr " } 6 x + 15 y = - 3$

$- 5 x - 3 y = 2 \text{ " stackrel (xx 5) rarr " } - 25 x - 15 y = 10$
$\textcolor{w h i t e}{X X X X X X X X X X X X X} \underline{\textcolor{w h i t e}{X X X X X X X X X X}}$

$\textcolor{w h i t e}{X X X X X X X X X X X X X X X} - 19 x = 7$

$\textcolor{w h i t e}{X X X X X X X X X X X X X X X X X X} \downarrow$

$\textcolor{w h i t e}{X X X X X X X X X X X X X X X X} x = - \frac{7}{19}$

Then from $2 x + 5 y = - 1$ we find:

$y = \frac{1}{5} \left(- 1 - 2 x\right)$

$\textcolor{w h i t e}{y} = \frac{1}{5} \left(- 1 - 2 \left(\textcolor{b l u e}{- \frac{7}{19}}\right)\right)$

$\textcolor{w h i t e}{y} = - \frac{1}{19}$