# How do solve the following linear system?:  5x-y=3 , x+y=-4 ?

Jul 12, 2016

$x = - \frac{1}{6} , \text{ } y = - 3 \frac{5}{6}$

#### Explanation:

An alternative method is to write each equation with y as the subject. Both equations allow this to be done easily.

$y = 5 x - 3 \text{ and } y = - x - 4$

And now by equating the $y$'s, we get
$y = y$

$\therefore 5 x - 3 = - x - 4$

$6 x = - 1 \Rightarrow \text{ } x = - \frac{1}{6}$

There are now two equations to calculate a value for $y$,which is quite nifty, because we can then check that each equation gives the same value for $y$.

$y = 5 \left(- \frac{1}{6}\right) - 3 = - 3 \frac{5}{6}$
$y = - \left(- \frac{1}{6}\right) - 4 = - 3 \frac{5}{6}$