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

Question

Savannah Anderson · Accepted Answer

#(5-x)/4# 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)#

Avery Alexander · Answer

undefined To solve for $ y $, first, combine like terms on both sides of the equation:

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

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

$$ 3x + 12y = 15 $$

Next, isolate the term containing $ y $ by subtracting $ 3x $ from both sides:

$$ 12y = 15 - 3x $$

Then, divide both sides by 12:

$$ y = \frac{15 - 3x}{12} $$

Thus, the solution for $ y $ is $ y = \frac{15 - 3x}{12} $.