SOLUTION: 4x-2y=4 -20x+10y=-20 is there no solution and does the graph only intersect at 1 point so the solution is unique?

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Question 278248: 4x-2y=4
-20x+10y=-20
is there no solution and does the graph only intersect at 1 point so the solution is unique?
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-2y=4%2C-20x%2B10y=-20%29


5%284x-2y%29=5%284%29 Multiply the both sides of the first equation by 5.


20x-10y=20 Distribute and multiply.


So we have the new system of equations:
system%2820x-10y=20%2C-20x%2B10y=-20%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:


%2820x-10y%29%2B%28-20x%2B10y%29=%2820%29%2B%28-20%29


%2820x%2B-20x%29%2B%28-10y%2B10y%29=20%2B-20 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.