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?

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by 5.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Since is always true, this means that there are an infinite number of solutions.

So the system is consistent and dependent.

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