Question

How do you solve this system of equations : `6x + 3y = 27 ; - 4x + 7y = 27`?

Answer 1

`x = 2, y= 5`

Explanation:

Hi there!

`6x + 3y = 27`
`-4x + 7y = 27`

We need to solve `6x + 3y = 27` for `x`
`6x = 27 - 3y`
Divide both sides by 6
`(6x)/6 = (27 - 3y)/6`
`x =(-1)/2 y + 9/2`
Now we need to substitute `(-1)/2 y + 9/2` for `x` in `-4x+7y=27`
`-4x + 7y = 27`
`-4(-1/2 y +9/2) + 7y = 27`
Simplify both sides
`9y - 18 = 27`
`9y = 27 + 18`
`9y = 45`
Divide both sides by `9`
`(9y)/9 = 45/9`
`y = 5`
Substitute `5` for `y` in `x = (-1)/2 y + 9/2`
`x = (-1)/2 y + 9/2`
`x = (-1)/2 (5) + 9/2`
Simplify
`x = 2`

Final answer : `x = 2` and `y=5`

I hope I helped!