SOLUTION: solve using the addition method x+y=8 -x+2y=7

Algebra ->  Systems-of-equations -> SOLUTION: solve using the addition method x+y=8 -x+2y=7      Log On


   

Question 365716: solve using the addition method
x+y=8
-x+2y=7
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=8%2C-x%2B2y=7%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%28-1x%2B2y%29=%288%29%2B%287%29


%281x%2B-1x%29%2B%281y%2B2y%29=8%2B7 Group like terms.


0x%2B3y=15 Combine like terms.


3y=15 Simplify.


y=%2815%29%2F%283%29 Divide both sides by 3 to isolate y.


y=5 Reduce.


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


x%2By=8 Now go back to the first equation.


x%2B5=8 Plug in y=5.


x=8-5 Subtract 5 from both sides.


x=3 Combine like terms on the right side.


So the solutions are x=3 and y=5.


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=8 (red) and -x%2B2y=7 (green)


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

Also, feel free to check out my tutoring website

Jim