SOLUTION: the solution set for x+y=2 and 2x+y=3

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Question 146851: the solution set for x+y=2 and 2x+y=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%2By=2%2C2x%2By=3%29


-2%28x%2By%29=-2%282%29 Multiply the both sides of the first equation by -2.


-2x-2y=-4 Distribute and multiply.


So we have the new system of equations:
system%28-2x-2y=-4%2C2x%2By=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:


%28-2x-2y%29%2B%282x%2By%29=%28-4%29%2B%283%29


%28-2x%2B2x%29%2B%28-2y%2B1y%29=-4%2B3 Group like terms.


0x-y=-1 Combine like terms. Notice how the x terms cancel out.


-y=-1 Simplify.


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


y=1 Reduce.


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-2x-2y=-4 Now go back to the first equation.


-2x-2%281%29=-4 Plug in y=1.


-2x-2=-4 Multiply.


-2x=-4%2B2 Add 2 to both sides.


-2x=-2 Combine like terms on the right side.


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


x=1 Reduce.


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


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 x%2By=2 (red) and 2x%2By=3 (green)