SOLUTION: x+y=10 x-y=2

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: x+y=10 x-y=2      Log On


   

Question 577136: x+y=10
x-y=2
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=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-1y%29=%2810%29%2B%282%29


%281x%2B1x%29%2B%281y%2B-1y%29=10%2B2 Group like terms.


2x%2B0y=12 Combine like terms. Notice how the y terms cancel out.


2x=12 Simplify.


x=%2812%29%2F%282%29 Divide both sides by 2 to isolate x.


x=6 Reduce.


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


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


6%2By=10 Plug in x=6.


6%2By=10 Multiply.


y=10-6 Subtract 6 from both sides.


y=4 Combine like terms on the right side.


So our answer is x=6 and y=4.


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=10 (red) and x-y=2 (green)