Question

How do you solve the following linear system: # –3x + 2y = 12 , 5x + 2y = -4 #?

Answer 1

`x = -2`
`y= 3`

Explanation:

1. The first step is to find similar coefficients between the two equations. Notice that both equations have a `2y` .

`-3x+ 2y =12`
`5x+ 2y =-4`

2. Because the coefficients are equal and not opposite, you have to times one of the equations by -1. For simplicity, lets use `-3x+ 2y =12`.

`-1*(-3x+ 2y =12)`
`5x+ 2y =-4`

`3x- 2y =-12`
`5x+ 2y =-4`

3. Now that the coefficients in front of `y` are opposite, we can add the two equations and the `y` values would cancel out.

`3x- 2y =-12`
`+`
`5x+ 2y =-4`

`8x=-16`

4. Divide both side by `8` to get the value of `x`.

`x=-2`

5. Substitute the value of `x` into one of the equations. For simplicity, lets use `5x+ 2y =-4` .

`5(-2)+ 2y =-4`

6. Simplify

`-10+ 2y =-4`

7. Add 10 to both sides so that `2y` is alone.

`2y=6`

8. Divide both side by `2` to get the value of `y`.

`y=3`

You now have found both the value of `x` and the value of `y`.

`x = -2`
`y= 3`