# How do you solve [(x+3y),(3x+y)]=[(-13),(1)]?

Jan 11, 2018

$x = 2$ and $y = - 5$

#### Explanation:

We can get two equations from the given:

(1) $x + 3 y = - 13$
(2) $3 x + y = 1$

If we multiply the second equation from $- 3$ we get:
$- 9 x - 3 y = - 3$. Adding this new equation to the first equation gives:

$- 8 x = - 16 \rightarrow x = 2$.

Taking this value of $x$ and substituting into (2) gives

$3 \left(2\right) + y = 1 \rightarrow 6 + y = 1 \rightarrow y = - 5$,

so $x = 2$ and $y = - 5$