SOLUTION: could someone help me determine whether the system has one solution, no solution, or infinitely many solutions for the following problems? y= -x+2 3x+3y=6 Also this problem:

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Question 29732: could someone help me determine whether the system has one solution, no solution, or infinitely many solutions for the following problems?
y= -x+2
3x+3y=6
Also this problem:
y= 2/3x
2x-y= -4
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1st problem:
Multiply the 1st equation by "3" to get:
3y=-3x+6
3y+3x=6
This is the same as the 2nd equatin.
So the two equations are really the same
line.
ONe line lies on top of the other. Therefore
there are an infinite number of solutions>
2nd Problem:
Solve the 1nd equatin for "y ot get:
y=2x+4
This line has a slope of 2 and an intercept of 4
The other equation has a slope of 2/3 and intercept of 0
The two lines are not the same; and they are not parallel;
they will intersect at one point.
Cheers,
Stan H.