Question

How do you solve the system of equations `x+ y = 55` and `40x + 20y = 1500`?

Answer 1

`x=20`
`y=35`

Explanation:

First, simplify the `40x+20y=1500` by dividing both sides by 20. The system becomes:

`2x+y=75`
`x+y=55`

Since `x+y=55`, y can be isolated in the equation, making it `y=55-x`.
Because this is a system of equations, both equations are true for the values of x and y, so we can substitute `55-x` in for y in `2x+y=75`.

`2x+55-x=75`

Simplify and solve for x.

`x+55=75`

`x=20`

Now that we know the x-value, it can be plugged into either one of the equations to get the y-value. Here, I used `x+y=55`.

`20+y=55`

`y=35`