Question

What is the x-value in the solution to the system `-6x - 5y = 10` & `3x - 2y= -6`?

Answer 1

`x=-50/27`

Explanation:

I'm going to use elimination to solve this set of equations.

`-6x-5y=10`
`+-`
`3x-2y=-6`

I want to add or subtract the `y`s so that I will be left with only `x` as my variaable. To do that, I need to make the `y`s equal, so I'm going to multiply the second equation by `2.5`, becauase that will change `-2y` into `-5y`. Of course, I have to multiply everything by `2.5`, so the second equation will now be `7.5x-5y=-15`.

Now we have
`color(white)(.....)-6xcancel(-5y)=10`
`-`
`color(white)(........)7.5xcancel(-5y)=-15`
`color(white)(.)`_____________
`color(white)(.....)-13.5x=color(white)(......)25`

We are left with `-13.5x=25`. Divide by `-13.5` on both sides, and we have `x=25/-13.5`, which we'll rewrite as `-50/27`.