SOLUTION: solve the system by the elimination method: x+9y=66 and -x+9y=60

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Question 236583: solve the system by the elimination method: x+9y=66 and -x+9y=60
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%28x%2B9y=66%2C-x%2B9y=60%29


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


%28x%2B9y%29%2B%28-1x%2B9y%29=%2866%29%2B%2860%29


%281x%2B-1x%29%2B%289y%2B9y%29=66%2B60 Group like terms.


0x%2B18y=126 Combine like terms.


18y=126 Simplify.


y=%28126%29%2F%2818%29 Divide both sides by 18 to isolate y.


y=7 Reduce.


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x%2B9y=66 Now go back to the first equation.


x%2B9%287%29=66 Plug in y=7.


x%2B63=66 Multiply.


x=66-63 Subtract 63 from both sides.


x=3 Combine like terms on the right side.


So the solutions are x=3 and y=7.


Which form the ordered pair .


This means that the system is consistent and independent.


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


Graph of x%2B9y=66 (red) and -x%2B9y=60 (green)