Question

Two times a number added to another number is 25. Three times the first number minus the other number is 20. How do you find the numbers?

Answer 1

`(x,y)=(9,7)`

Explanation:

We have two numbers, `x, y`. We know two things about them:

`2x+y=25`

`3x-y=20`

Let's add these two equations together which will cancel the `y`:

`5x+0y=45`

`x=45/5=9`

We can now substitute in the `x` value into one of the original equations (I'll do both) to get to `y`:

`2x+y=25`

`2(9)+y=25`

`18+y=25`

`y=7`

`3x-y=20`

`3(9)-y=20`

`27-y=20`

`y=7`