SOLUTION: Solve by using the elimination method: 4x + 5y = 3 8x + 10y = 6 What is the solution of the system?

Algebra ->  Expressions-with-variables -> SOLUTION: Solve by using the elimination method: 4x + 5y = 3 8x + 10y = 6 What is the solution of the system?      Log On


   

Question 190638: Solve by using the elimination method:
4x + 5y = 3
8x + 10y = 6
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%284x%2B5y=3%2C8x%2B10y=6%29


-2%284x%2B5y%29=-2%283%29 Multiply the both sides of the first equation by -2.


-8x-10y=-6 Distribute and multiply.


So we have the new system of equations:
system%28-8x-10y=-6%2C8x%2B10y=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:


%28-8x-10y%29%2B%288x%2B10y%29=%28-6%29%2B%286%29


%28-8x%2B8x%29%2B%28-10y%2B10y%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.