SOLUTION: solve by the elimination method 2x=3y=1 4x+6y=2 what is the solution of the system

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Question 146585: solve by the elimination method
2x=3y=1
4x+6y=2
what is the solution of the system
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%2B3y=1%2C4x%2B6y=2%29


-2%282x%2B3y%29=-2%281%29 Multiply the both sides of the first equation by -2.


-4x-6y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-4x-6y=-2%2C4x%2B6y=2%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:


%28-4x-6y%29%2B%284x%2B6y%29=%28-2%29%2B%282%29


%28-4x%2B4x%29%2B%28-6y%2B6y%29=-2%2B2 Group like terms.


0x%2B0y=0 Combine like terms.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions. So the two equations are consistent and dependent.