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

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Question 557490: x-3y=2
x+2y=-3
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-3y=2%2Cx%2B2y=-3%29


-1%28x-3y%29=-1%282%29 Multiply the both sides of the first equation by -1.


-1x%2B3y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-1x%2B3y=-2%2Cx%2B2y=-3%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:


%28-1x%2B3y%29%2B%28x%2B2y%29=%28-2%29%2B%28-3%29


%28-1x%2B1x%29%2B%283y%2B2y%29=-2%2B-3 Group like terms.


0x%2B5y=-5 Combine like terms.


5y=-5 Simplify.


y=%28-5%29%2F%285%29 Divide both sides by 5 to isolate y.


y=-1 Reduce.


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-1x%2B3y=-2 Now go back to the first equation.


-1x%2B3%28-1%29=-2 Plug in y=-1.


-x-3=-2 Multiply.


-x=-2%2B3 Add 3 to both sides.


-x=1 Combine like terms on the right side.


x=%281%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-1 Reduce.


So the solutions are x=-1 and y=-1.


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

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Jim