SOLUTION: Solve by the elimination method? 6x - 4y = 62 3x + 6y = -9 What is the solution of the method? (Type an order pair. Simplify your answer?)

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Question 157505: Solve by the elimination method?

6x - 4y = 62
3x + 6y = -9
What is the solution of the method?
(Type an order pair. Simplify your answer?)
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-4y=62%2C3x%2B6y=-9%29


-2%283x%2B6y%29=-2%28-9%29 Multiply the both sides of the second equation by -2.


-6x-12y=18 Distribute and multiply.


So we have the new system of equations:
system%286x-4y=62%2C-6x-12y=18%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-4y%29%2B%28-6x-12y%29=%2862%29%2B%2818%29


%286x%2B-6x%29%2B%28-4y%2B-12y%29=62%2B18 Group like terms.


0x%2B-16y=80 Combine like terms. Notice how the x terms cancel out.


-16y=80 Simplify.


y=%2880%29%2F%28-16%29 Divide both sides by -16 to isolate y.


y=-5 Reduce.


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6x-4y=62 Now go back to the first equation.


6x-4%28-5%29=62 Plug in y=-5.


6x%2B20=62 Multiply.


6x=62-20 Subtract 20 from both sides.


6x=42 Combine like terms on the right side.


x=%2842%29%2F%286%29 Divide both sides by 6 to isolate x.


x=7 Reduce.


So our answer is 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 6x-4y=62 (red) and 3x%2B6y=-9 (green)


Questions? Email me at jim_thompson5910@hotmail.com