Question

How do you solve the system of equations `y= 2x - 7` and `5x + 3y = 34`?

Answer 1

`x=5` and `y=3`

Explanation:

`y=2x-7`
`5x+3y=34`

Using the value of `y` from the first equation, replace `y` in the second equation with `color(blue)((2x-7))`.

`5x+3y=34`

`5x+3color(blue)((2x-7))=34`

Open the brackets and simplify.

`5x+color(blue)(6x-21)=34`

`11x-21=34`

Add `21` to each side.

`11x-21+21=34+21`

`11x=55`

Divide both sides by `11`.

`(11x)/11=55/11`

`(cancel11x)/(cancel11)=5`

`x=5`

In the first equation, replace `x` with `color(red)5`.

`y=2x-7`

`y=2(color(red)5)-7`

`y=10-7`

`y=3`