SOLUTION: -7x+6y=59 -8x+6y=58

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Question 146544: -7x+6y=59
-8x+6y=58
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%28-7x%2B6y=59%2C-8x%2B6y=58%29


-1%28-8x%2B6y%29=-1%2858%29 Multiply the both sides of the second equation by -1.


8x-6y=-58 Distribute and multiply.


So we have the new system of equations:
system%28-7x%2B6y=59%2C8x-6y=-58%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:


%28-7x%2B6y%29%2B%288x-6y%29=%2859%29%2B%28-58%29


%28-7x%2B8x%29%2B%286y%2B-6y%29=59%2B-58 Group like terms.


x%2B0y=1 Combine like terms. Notice how the y terms cancel out.


x=1 Simplify.


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-7x%2B6y=59 Now go back to the first equation.


-7%281%29%2B6y=59 Plug in x=1.


-7%2B6y=59 Multiply.


6y=59%2B7 Add 7 to both sides.


6y=66 Combine like terms on the right side.


y=%2866%29%2F%286%29 Divide both sides by 6 to isolate y.


y=11 Reduce.


So our answer is x=1 and y=11.


Which form the ordered pair .


This means that the two equations are consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of -7x%2B6y=59 (red) and -8x%2B6y=58 (green)