Question

How do you solve the system 4x-5y=-43 , 6x+71=y?

Answer 1

`x = 12 and y = 143`

Equate your `y` value to the first equation.*

Cancel out `5y` and find the value of `x`

Substitute the value for `x` into either of the two equations and solve for `y`

Explanation:

Transpose `4x - 5y = -43" "` into `" "5y = 4x + 43`
Multiply the second equation, `" "y = 6x + 71" "` by `" "5` to get:

`5y = 30x+355`

*You'll end up with two equations:

`5y = 4x + 43`
And
`5y = 30x + 355`

Thus,
`4x + 43 = 30x + 355`

Transpose your variables and constants and you'll get:

`30x - 4x = 355 - 43`

`26x = 312`

`x = 312/26`

`x = 12`

Solve for `y` since `x = 12,`

Use either of the two equations given, I'll use `y = 6x + 71`

`y = (6 x 12) + 71`

`y = 143`

`x = 12 and y = 143`