# How do solve the following linear system?:  x + y= 12 , 3x + y = -20 ?

Mar 23, 2016

line up the system of equations making sure that the variables are in the same relative positions.
$\frac{x + y = 12. e q .1}{3 x + y = - 20 . e q .2}$

subtract equation 2 from equation 1
this will eliminate the y variable since they both have the same coefficient and same sign.

$- 2 x = 32$

solve for x
x = -16

now substitute the value for x into either the first or second equation (doesn't matter). A good choice would be to pick the simplest equation of the two and this looks like equation 1.
By substituting x = -16 into eqn,1, you will now be able to solve for the y value.

Mar 23, 2016

$x = - 16$
$y = 28$

#### Explanation:

$x = - 16$
$y = 28$