# How do you solve the following system?: 6x +5y =-1 , -5x -9y = 5

Mar 24, 2018

$x = \frac{16}{29}$
$y = - \frac{25}{29}$

#### Explanation:

For solving using substitution method you have to separate out the value of any one variable $\left(x \mathmr{and} y\right)$ in any of the equation and put it in the other equation.
Assuming $6 x + 5 y = - 1$ to be equation $1$ and $- 5 x - 9 y = 5$ be equation $2$
Seperating out the value of $x$
$x = \frac{- 1 - 5 y}{6}$ and now putting it in the second equation
$- 5 \left(\frac{- 1 - 5 y}{6}\right) - 9 y = 5$
$5 \left(\frac{1 + 5 y}{6}\right) - 9 y = 5$
$\left(\frac{5 + 25 y}{6}\right) - 9 y = 5$
Now on taking $L C M$ on LHS
$\left(\frac{5 + 25 y - 54 y}{6}\right) = 5$
$\left(5 + 25 y - 54 y\right) = 30$
$5 - 29 y = 30$
$29 y = - 25$
$y = - \frac{25}{29}$
Now put the value of $y$ in any of the two equations
$\left(6 x + 5 \left(- \frac{25}{29}\right)\right) = - 1$
$\left(6 x - \frac{125}{29}\right) = - 1$
$6 x = \frac{125}{29} - 1$
$6 x = \frac{125 - 29}{29}$
$6 x = \frac{96}{29}$
$x = \frac{16}{29}$