Question

How do you solve the system of equations `3x - 4y = - 18` and `20x + 17y = 11`?

Answer 1

`x=-2`, `y=3`

Explanation:

We have a system of equations:
`color(white)(-)3x-4y=-18`
`color(white)(-)`
`color(white)(-)20x+17y=11`

I usually like to use elimination for these problems,. Sometimes variables are easily eliminated, but in this case, we'll need to change the coeffiecients. We can either multiply or divide, and personally, I prefer multiplication.

If we multiply `(3x-4y=-18)` by `4.25`, `-4y` becomes `-17y`. That would allow us to add the two equations and remove the `y`s.

`4.25*` `color(white)(-)(3x-4y=-18)`
`color(white)(-)`
`color(white)(-)color(white)(4.25*)20x+17y=11`

`color(white)(+)12.75xcancel(-17y)=-76.5`
`color(black)(+)`
`color(white)(+)20x+cancel(17x)=11`.
...............................................
`32.75x=-65.5`
divide by `32.75` on both sides

`x=-2`

Now let's solve for `y` by replacing `x` with `-2`.

`3x-4y=-18`
`3(-2)-4y=-18`
`-6-4y=-18`

add `6` on both sides

`-4y=-12`

divide by `-4` on both sides

`y=3`

We have our `x` and `y` values, but just to double-check our work, let's solve the other equation using `-2` and `3` instead of `x` and `y`.

`20x+17x=11`
`20(-2)+17(3)` should equal `11`
`-40+51`
`11=11`

We were right; our values were correct! Nice work