Question

How do you solve the following system?: `5x-7y=22 , 3x+3y=-21`

Answer 1

`(x,y)=(-9/4,-19/4)`

Explanation:

We have

`5x-7y=22`
`3x+3y=-21`

Let's notice that we can divide the second equation by 3:

`x+y=-7`

I'll solve for `x`:

`x=-7-y`

And now substitute into the first equation:

`5(-7-y)-7y=22`

`-35-5y-7y=22`

`-12y=57`

`y=-57/12=-19/4`

`:. 3x+3(-19/4)=-21`

`3x-57/4=-21`

`12x-57=-84`

`12x=-27=>x=-27/12=-9/4`

Graphed, it looks like this:

graph{(5x-7y-22)(3x+3y+21)=0[-10,10,-10,0]}

(On my screen, the graphing utility is sometimes cutting off one part of one of lines. To fix, hover over the graph and zoom in/out and that seems to fix it).