SOLUTION: Using the addition method 7x-4y=14 -7x+6y=11

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Question 275008: Using the addition method
7x-4y=14
-7x+6y=11
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%287x-4y=14%2C-7x%2B6y=11%29


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


%287x-4y%29%2B%28-7x%2B6y%29=%2814%29%2B%2811%29


%287x%2B-7x%29%2B%28-4y%2B6y%29=14%2B11 Group like terms.


0x%2B2y=25 Combine like terms.


2y=25 Simplify.


y=%2825%29%2F%282%29 Divide both sides by 2 to isolate y.


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7x-4y=14 Now go back to the first equation.


7x-4%2825%2F2%29=14 Plug in y=25%2F2.


7x-50=14 Multiply.


7x=14%2B50 Add 50 to both sides.


7x=64 Combine like terms on the right side.


x=%2864%29%2F%287%29 Divide both sides by 7 to isolate x.


So the solutions are x=64%2F7 and y=25%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.