SOLUTION: Solve each system by addition x+y = 7 x-y =9

Algebra ->  Graphs -> SOLUTION: Solve each system by addition x+y = 7 x-y =9      Log On


   

Question 246061: Solve each system by addition
x+y = 7
x-y =9
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=7%2Cx-y=9%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=%287%29%2B%289%29


%28x%2Bx%29%2B%28y-y%29=7%2B9 Group like terms.


2x%2B0y=16 Combine like terms.


2x=16 Simplify.


x=%2816%29%2F%282%29 Divide both sides by 2 to isolate x.


x=8 Reduce.


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


x%2By=7 Now go back to the first equation.


8%2By=7 Plug in x=8.


y=7-8 Subtract 8 from both sides.


y=-1 Combine like terms on the right side.


So the solutions are x=8 and y=-1.


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=7 (red) and x-y=9 (green)