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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
3x%2B3y=6
y=-x%2B2



3x%2B3%28-x%2B2%29=6 Plug in y=-x%2B2 into the first equation. In other words, replace each y with -x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


3x%2B-x%2B6=6 Distribute


2x%2B6=6 Combine like terms on the left side


2x=6-6Subtract 6 from both sides


2x=0 Combine like terms on the right side


x=%280%29%2F%282%29 Divide both sides by 2 to isolate x



x=0 Divide




Now that we know that x=0, we can plug this into y=-x%2B2 to find y



y=-%280%29%2B2 Substitute 0 for each x


y=2 Simplify


So our answer is x=0 and y=2
So the system has one solution