SOLUTION: Determine whether the system has one solution, no solution, or infinitely many solutions: y=-x+2 3x+3y=6

Question 111721: Determine whether the system has one solution, no solution, or infinitely many solutions: y=-x+2 3x+3y=6
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Subtract 6 from both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and
So the system has one solution
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