SOLUTION: Solve each system by the addition method. Determine whether the equations are independent, dependent, or inconsistent. x-y=3 -6x+6y=17

Question 175923: Solve each system by the addition method. Determine whether the equations are independent, dependent, or inconsistent.
x-y=3
-6x+6y=17
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 6.

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 NEVER true, this means that there are no solutions.

So the system is inconsistent.

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