SOLUTION: x + y = 16 x-y=-2 What is the solution of this system?

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Question 208094: x + y = 16
x-y=-2
What is the solution of this system?
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=16%2Cx-y=-2%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%2By%29%2B%28x-y%29=%2816%29%2B%28-2%29


%28x%2Bx%29%2B%28y-y%29=16-2 Group like terms.


2x%2B0y=14 Combine like terms.


2x=14 Simplify.


x=%2814%29%2F%282%29 Divide both sides by 2 to isolate x.


x=7 Reduce.


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x%2By=16 Now go back to the first equation.


7%2By=16 Plug in x=7.


y=16-7 Subtract 7 from both sides.


y=9 Combine like terms on the right side.


So the solutions are x=7 and y=9.


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=16 (red) and x-y=-2 (green)