Question

How do you find an ordered pair for 3x - 4y = 18 and 5y = x - 28?

Answer 1

Solve for x in one equation in order to substitute it into the other equation and you'll work through to get (-2,-6)

Explanation:

Let's start with the original equations:

`3x-4y=18`
`5y=x-28`

We can solve the 2nd equation for x, then substitute that into the first equation. So let's first take the 2nd equation:

`5y=x-28`

and add 28 to both sides to get:

`x=5y+28`

We can now substitute that into the first equation:

`3x-4y=18`

`3(5y+28)-4y=18`

now let's solve for y:

`15y+84-4y=18`

`11y=-66`

`y=-6`

We can now substitute in the y value into one of our equations to find the x value. I'm going to use

`x=5y+28`

`x=5(-6)+28`

`x=-2`

Now let's check the answer:

`3x-4y=18`

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

`-6+24=18` check!

`5y=x-28`

`5(-6)=(-2)-28`

`-30=-2-28` check!

So the final answer is (-2,-6)