SOLUTION: x+2y=9 -x-3y=-12

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Question 595229: x+2y=9 -x-3y=-12
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%2B2y=9%2C-x-3y=-12%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%2B2y%29%2B%28-x-3y%29=%289%29%2B%28-12%29


%28x-x%29%2B%282y-3y%29=9%2B-12 Group like terms.


0x-y=-3 Combine like terms.


-y=-3 Simplify.


y=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=3 Reduce.


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x%2B2y=9 Now go back to the first equation.


x%2B2%283%29=9 Plug in y=3.


x%2B6=9 Multiply.


x=9-6 Subtract 6 from both sides.


x=3 Combine like terms on the right side.


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


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%2B2y=9 (red) and -x-3y=-12 (green)