SOLUTION: I need your help figuring out how to solve 4x+3y=4 and 6x-6y=-1 by elimination.

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Question 209718This question is from textbook
: I need your help figuring out how to solve 4x+3y=4 and 6x-6y=-1 by elimination. This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%284x%2B3y=4%2C6x-6y=-1%29


2%284x%2B3y%29=2%284%29 Multiply the both sides of the first equation by 2.


8x%2B6y=8 Distribute and multiply.


So we have the new system of equations:
system%288x%2B6y=8%2C6x-6y=-1%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%288x%2B6y%29%2B%286x-6y%29=%288%29%2B%28-1%29


%288x%2B6x%29%2B%286y%2B-6y%29=8%2B-1 Group like terms.


14x%2B0y=7 Combine like terms.


14x=7 Simplify.


x=%287%29%2F%2814%29 Divide both sides by 14 to isolate x.


x=1%2F2 Reduce.


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8x%2B6y=8 Now go back to the first equation.


8%281%2F2%29%2B6y=8 Plug in x=1%2F2.


4%2B6y=8 Multiply.


6y=8-4 Subtract 4 from both sides.


6y=4 Combine like terms on the right side.


y=%284%29%2F%286%29 Divide both sides by 6 to isolate y.


y=2%2F3 Reduce.


So the solutions are x=1%2F2 and y=2%2F3.


Which form the ordered pair .


This means that the system is consistent and independent.