SOLUTION: Solve by the elimination method. x+3y=14 -x+7y=6

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve by the elimination method. x+3y=14 -x+7y=6      Log On


   

Question 243528: Solve by the elimination method.
x+3y=14
-x+7y=6
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%2B3y=14%2C-x%2B7y=6%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%2B3y%29%2B%28-x%2B7y%29=%2814%29%2B%286%29


%28x-x%29%2B%283y%2B7y%29=14%2B6 Group like terms.


0x%2B10y=20 Combine like terms.


10y=20 Simplify.


y=%2820%29%2F%2810%29 Divide both sides by 10 to isolate y.


y=2 Reduce.


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


x%2B3y=14 Now go back to the first equation.


x%2B3%282%29=14 Plug in y=2.


x%2B6=14 Multiply.


x=14-6 Subtract 6 from both sides.


x=8 Combine like terms on the right side.


So the solutions are x=8 and y=2.


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%2B3y=14 (red) and -x%2B7y=6 (green)