SOLUTION: 2x+y=10 6x+3y=30

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Question 218385: 2x+y=10
6x+3y=30
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%282x%2By=10%2C6x%2B3y=30%29


-3%282x%2By%29=-3%2810%29 Multiply the both sides of the first equation by -3.


-6x-3y=-30 Distribute and multiply.


So we have the new system of equations:
system%28-6x-3y=-30%2C6x%2B3y=30%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:


%28-6x-3y%29%2B%286x%2B3y%29=%28-30%29%2B%2830%29


%28-6x%2B6x%29%2B%28-3y%2B3y%29=-30%2B30 Group like terms.


0x%2B0y=0 Combine like terms. Notice how the x terms cancel out.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions.


So the system is consistent and dependent.