SOLUTION: 2x+y=10 6x+3y=30

Question 218385: 2x+y=10
6x+3y=30
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 -3.

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. Notice how the x terms cancel out.

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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