SOLUTION: What is the solution to this system of equations: x + y = 10 x – y = 22

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Question 365757: What is the solution to this system of equations:

x + y = 10
x – y = 22
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=10%2Cx-y=22%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-1y%29=%2810%29%2B%2822%29


%281x%2B1x%29%2B%281y%2B-1y%29=10%2B22 Group like terms.


2x%2B0y=32 Combine like terms.


2x=32 Simplify.


x=%2832%29%2F%282%29 Divide both sides by 2 to isolate x.


x=16 Reduce.


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x%2By=10 Now go back to the first equation.


16%2By=10 Plug in x=16.


y=10-16 Subtract 16 from both sides.


y=-6 Combine like terms on the right side.


So the solutions are x=16 and y=-6.


Which form the ordered pair .


This means that the system is consistent and independent.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim