SOLUTION: System of equations. x+y=3 2x+y=4

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Question 407336: System of equations.
x+y=3
2x+y=4
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=3%2C2x%2By=4%29


-1%282x%2By%29=-1%284%29 Multiply the both sides of the second equation by -1.


-2x-1y=-4 Distribute and multiply.


So we have the new system of equations:
system%28x%2By=3%2C-2x-1y=-4%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:


%28x%2By%29%2B%28-2x-1y%29=%283%29%2B%28-4%29


%281x%2B-2x%29%2B%281y%2B-1y%29=3%2B-4 Group like terms.


-x%2B0y=-1 Combine like terms. Notice how the y terms cancel out.


-x=-1 Simplify.


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


x=1 Reduce.


------------------------------------------------------------------


x%2By=3 Now go back to the first equation.


1%2By=3 Plug in x=1.


1%2By=3 Multiply.


y=3-1 Subtract 1 from both sides.


y=2 Combine like terms on the right side.


So our answer is x=1 and y=2.


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%2By=3 (red) and 2x%2By=4 (green)


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Jim