Question

How do you solve for y `9x + 3y - 5 = 6x - 9y + 10`?

Answer 1

`(5-x)/4`

Explanation:

Your goal here is to isolate `y` on one side of the equation.

This implies that you need to have all the `x`-terms and all the integers on the other side of the equation. Your starting equation looks like this

`9x + 3y - 5 = 6x - 9y + 10`

Start by adding `5` to both sides of the equation

`9x + 3y - color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) = 6x - 9y + 10 + 5`

`9x + 3y = 6x - 9y + 15`

Next, add `9y` to both sides of the equation

`9x + 3y + 9y = 6x - color(red)(cancel(color(black)(9y))) + color(red)(cancel(color(black)(9y))) + 15`

`9x + 12y = 6x + 15`

Next, add `-9x` to both sides

`color(red)(cancel(color(black)(9x))) - color(red)(cancel(color(black)(9x))) + 12y = 6x - 9x + 15`

`12y = -3x + 15`

Finally, divide both sides by `12` and simplify where possible

`(color(red)(cancel(color(black)(12)))y)/color(red)(cancel(color(black)(12))) = (-3x + 15)/12`

`y = color(green)((5-x)/4)`