# How do you solve the following system?: -x -2y =1, 9x -y = -1

Nov 14, 2015

We can solve this question by finding the value of x with respect to y from both equations. Since the value of x should be equal, the equations thus obtained can be solved for y. And then either of the initial equations can be used to find x.

#### Explanation:

1. $- x - 2 y$ = 1 => $- x = 1 + 2 y$ => $x = - \left(1 + 2 y\right)$ ----EQUATION 1
2. $9 x - y = - 1$ => $9 x = y - 1$ => $x = \frac{1}{9} \cdot \left(y - 1\right)$ ----EQUATION 2

Equating the values of x from EQUATION 1 and EQUATION 2;
we have;
$- \left(1 + 2 y\right) = \frac{1}{9} \cdot \left(y - 1\right)$
=> $- 9 - 18 y = y - 1$
=>$- 18 y - y = - 1 + 9$
=>$- 19 y = 8$
=>$y = - \frac{8}{19}$

Using EQUATION 1;
$x = - \left(1 + 2 y\right)$
=>$x = - \left(1 + 2 \cdot \left(- \frac{8}{19}\right)\right)$
=>$x = - \left(1 - \frac{16}{19}\right)$
=>$x = - \frac{3}{19}$

So there you have it!!

$x = - \frac{3}{19}$
and
$y = - \frac{8}{19}$