Question

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

Answer 1

line up the system of equations making sure that the variables are in the same relative positions.
`(x+y=12. eq.1)/(3x+y=-20 . eq.2)`

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

`-2x=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.

Answer 2

`x=-16`
`y=28`

Explanation:

`x=-16`
`y=28`