SOLUTION: 2x+3y=3 4x+6y=6 What is the solution of the system? (type an ordered pair. type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many s

Algebra ->  Linear-equations -> SOLUTION: 2x+3y=3 4x+6y=6 What is the solution of the system? (type an ordered pair. type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many s      Log On


   

Question 183761: 2x+3y=3
4x+6y=6
What is the solution of the system?
(type an ordered pair. type an integer or a fraction. Type N if there is no solution. Type I if there are infinitely many solutions)
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=3%2C4x%2B6y=6%29


-2%282x%2B3y%29=-2%283%29 Multiply the both sides of the first equation by -2.


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


So we have the new system of equations:
system%28-4x-6y=-6%2C4x%2B6y=6%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=%28-6%29%2B%286%29


%28-4x%2B4x%29%2B%28-6y%2B6y%29=-6%2B6 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 system is consistent and dependent.