Question

How do you solve the system of equations `x+ 5y = - 7` and `6x - 8y = - 24`?

Answer 1

`color(blue)(ul(bar(abs(color(black)(-88/19,-9/19)))))`

Explanation:

One way to do it is to use substitution. I'll take the equation `x+5y=-7` and solve for `x`:

`x=-5y-7`

and now I'll substitute it into our other equation:

`6x-8y=-24`

`6(-5y-7)-8y=-24`

`-30y-42-8y=-24`

`-38y=18`

`y=-18/38=-9/19`

And now let's substitute in and solve for `x`:

`x+5y=-7`

`x+5(-9/19)=-7`

`x-45/19=-7`

`x=-7+45/19=-7(19/19)+45/19=-133/19+45/19=-88/19`

and let's check the other as well:

`6x-8y=-24`

`6x-8(-9/19)=-24`

`6x+72/19=-24`

`6x=-24(19/19)-72/19`

`x=((-456-72)/19)/6=(-528/19)/6=-528/(19xx6)=-88/19`

Our solution then is:

`color(blue)(ul(bar(abs(color(black)(-88/19,-9/19)))))`

We can see this point here:

graph{(6x-8y+24)(x+5y+7)=0 [-15, 5, -5, 5]}