SOLUTION: Solve by the elimination method x+2y=17 -x+6y=23

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve by the elimination method x+2y=17 -x+6y=23      Log On


   

Question 200629: Solve by the elimination method
x+2y=17
-x+6y=23
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%2B2y=17%2C-x%2B6y=23%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%2B2y%29%2B%28-x%2B6y%29=%2817%29%2B%2823%29


%28x-x%29%2B%282y%2B6y%29=17%2B23 Group like terms.


0x%2B8y=40 Combine like terms.


8y=40 Simplify.


y=%2840%29%2F%288%29 Divide both sides by 8 to isolate y.


y=5 Reduce.


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


x%2B2y=17 Now go back to the first equation.


x%2B2%285%29=17 Plug in y=5.


x%2B10=17 Multiply.


x=17-10 Subtract 10 from both sides.


x=7 Combine like terms on the right side.


So the solutions are x=7 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%2B2y=17 (red) and -x%2B6y=23 (green)