How do you solve for y in $3+6x = 11-4y$ ?

Question

3827 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-20T14:30:53

See the entire solution process below:

First, subtract $color(red)(11)$ from each side of the equation to isolate the $y$ term while keeping the equation balanced:

$-color(red)(11) + 3 + 6x = -color(red)(11) + 11 - 4y$

$-8 + 6x = 0 - 4y$

$-8 + 6x = -4y$

Now, divide each side of the equation by $color(red)(-4)$ to solve for $y$ while keeping the equation balanced:

$(-8 + 6x)/color(red)(-4) = (-4y)/color(red)(-4)$

$(-8)/color(red)(-4) + (6x)/color(red)(-4) = (color(red)(cancel(color(Black)(-4)))y)/cancel(color(red)(-4))$

$2 - 6/4x = y$

$2 - (2 xx 3)/(2 xx 2)x = y$

$2 - (color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 2)x = y$

$2 - 3/2/x = y$

$y = 2 - 3/2x$

Or

$y = -3/2x + 2$

How do you solve for y in 3+6x = 11-4y3+6x = 11-4y?