SOLUTION: Solve by the addition method? 6x - y = 49 x + 6y = 39 What is the solution of the system? (Simplify you answer. Type an order pair?)

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve by the addition method? 6x - y = 49 x + 6y = 39 What is the solution of the system? (Simplify you answer. Type an order pair?)      Log On


   

Question 157504: Solve by the addition method?
6x - y = 49
x + 6y = 39
What is the solution of the system?
(Simplify you answer. Type an order pair?)
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%286x-y=49%2Cx%2B6y=39%29


-6%28x%2B6y%29=-6%2839%29 Multiply the both sides of the second equation by -6.


-6x-36y=-234 Distribute and multiply.


So we have the new system of equations:
system%286x-1y=49%2C-6x-36y=-234%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%286x-1y%29%2B%28-6x-36y%29=%2849%29%2B%28-234%29


%286x%2B-6x%29%2B%28-1y%2B-36y%29=49%2B-234 Group like terms.


0x%2B-37y=-185 Combine like terms. Notice how the x terms cancel out.


-37y=-185 Simplify.


y=%28-185%29%2F%28-37%29 Divide both sides by -37 to isolate y.


y=5 Reduce.


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6x-1y=49 Now go back to the first equation.


6x-1%285%29=49 Plug in y=5.


6x-5=49 Multiply.


6x=49%2B5 Add 5 to both sides.


6x=54 Combine like terms on the right side.


x=%2854%29%2F%286%29 Divide both sides by 6 to isolate x.


x=9 Reduce.


So our answer is x=9 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 6x-y=49 (red) and x%2B6y=39 (green)


Questions? Email me at jim_thompson5910@hotmail.com