Question

How do you solve these equations with the elimination method?

`-4x--y=14` and `3x-9y=-18`

Answer 1

`(-36/11,10/11)`

Explanation:

Our equations are as follows:

`-4x+y=14`
`3x-9y=-18`

When we solve equations by elimination, we want to get rid of one variables. The easiest will be `y`.

Let's multiply the first equation by `9`. Thus, our new system is

`-36x+color(blue)(9y)=126`
`3xcolor(blue)(-9y)=-18`

What do you notice? The `y` terms will cancel. We can add these two systems and get

`-33x=108`

Dividing both sides by `-33`, we get

`x=-36/11`

We have solved for one variable, so we can solve for the other. We can plug this in for `x` in the second equation to get

`3(-36/11)-9y=-18`

`=>-108/11-9y=-18`

We can multiply both the `-9y` and the `-18` by `11/11` to achieve a common denominator. We get

`-108/11-99/11y=-198/11`

Adding `-108/11` to both sides, we get

`-99/11y=-90/11`

Let's multiply both sides by `-11` to get

`99y=90`

Dividing both sides by `99`, we get

`y=90/99`

which can be simplified to

`y=10/11`

Thus, the solution of this system is

`(-36/11,10/11)`

Hope this helps!