# How do you solve the following system?: -x -6y =-1, 3x -y = -4

Nov 17, 2015

See explanation

#### Explanation:

Isolate one variable in one the equations. Then use the resulting equivalent to replace the same variable in the other equation

$- x - 6 y = - 1$
$3 x - y = - 4$

If we isolate $x$ in the first equation, we will have

$- x - 6 y = - 1$
$\implies x = - 6 y + 1$

Now, let's replace $x$ in the second equation

$3 x - y = - 4$
$\implies 3 \left(- 6 y + 1\right) - y = - 4$
$\implies - 18 y + 3 - y = - 4$
$\implies - 19 y + 3 = - 4$
$\implies - 19 y = - 7$
$\implies y = \frac{7}{19}$

Now that we have the value for $y$, substitute it into any of the equalities above to get $x$

$x = - 6 y + 1$
$\implies x = - 6 \left(\frac{7}{19}\right) + 1$
$\implies x = - \frac{42}{19} + 1$

$\implies x = \frac{- 42 + 19}{19}$

$\implies x = - \frac{23}{19}$