SOLUTION: 2x+y=4 x+y+2 im stuck i need help solving this can you give me some help

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Question 154416: 2x+y=4
x+y+2
im stuck i need help solving this can you give me some help
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%282x%2By=4%2Cx%2By=2%29


-1%28x%2By%29=-1%282%29 Multiply the both sides of the second equation by -1.


-x-y=-2 Distribute and multiply.


So we have the new system of equations:
system%282x%2By=4%2C-x-y=-2%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:


%282x%2By%29%2B%28-x-y%29=%284%29%2B%28-2%29


%282x-x%29%2B%28y-y%29=4%2B-2 Group like terms.


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


x=2 Simplify.


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2x%2By=4 Now go back to the first equation.


2%282%29%2By=4 Plug in x=2.


4%2By=4 Multiply.


y=4-4 Subtract 4 from both sides.


y=0 Combine like terms on the right side.


So our answer is x=2 and y=0.


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