Question

How do you solve for y given `2x+3y-11=0`?

Answer 1

See the full explanation below

Explanation:

Step 1) Add and subtract the necessary terms from each side of the equation to isolate the `y` term while keeping the equation balanced:

`2x + 3y - 11 - color(red)(2x) + color(blue)(11) = 0 - color(red)(2x) + color(blue)(11)`

`2x - color(red)(2x) + 3y - 11 + color(blue)(11) = 0 - color(red)(2x) + color(blue)(11)`

`0 + 3y - 0 = -2x + 11`

`3y = -2x + 11`

Step 2) Divide each side of the equation by `color(red)(3)` to solve for `y` while keeping the equation balanced:

`(3y)/color(red)(3) = (-2x + 11)/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = -2/color(red)(3)x + 11/color(red)(3)`

`y = -2/3x + 11/3`