SOLUTION: Solve by the elimination method 2x+3y=2 4x+6y=4

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve by the elimination method 2x+3y=2 4x+6y=4      Log On


   

Question 146611: Solve by the elimination method
2x+3y=2
4x+6y=4
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=2%2C4x%2B6y=4%29


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


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


So we have the new system of equations:
system%28-4x-6y=-4%2C4x%2B6y=4%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=%28-4%29%2B%284%29


%28-4x%2B4x%29%2B%28-6y%2B6y%29=-4%2B4 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 two equations are consistent and dependent.