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

Sep 4, 2016

$x = 3$ and $y = - 6$

#### Explanation:

There are many methods for solving pair of linear equations in two variables. Prominent among them is substitution method.

First equation $x + y = - 3$ gives us $x = - y - 3$. Putting this in second equation we get

3×(-y-3)+y=3 or

$- 3 y - 9 + y = 3$ or

$- 2 y = 3 + 9 = 12$ i.e. $y = - 6$ and $x = - \left(- 6\right) - 3 = 6 - 3 = 3$

Another method could be multiplying first equation by $3$ which gives us $3 x + 3 y = - 9$. Now subtracting second equation $3 x + y = 3$ from this, we get $2 y = - 12$ or $y = - 6$. Putting this in first we get $x - 6 = - 3$ i.e. $x = 3$.