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

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Answer 1 · 2017-01-08T16:06:16

See the full explanation below

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#