SOLUTION: Can anyone help me with this problem? Solve each of the following systems, if possible. Indicate whether the system has a unique solution, infinitely many solutions or no solut

Question 326701: Can anyone help me with this problem?
Solve each of the following systems, if possible. Indicate whether the system has a unique solution, infinitely many solutions or no solution.
(a)3y = x � 10
y = x � 2
(b)x + y = 5
3x + 3y = 15
Am I graphing this since they're systems? Am I substituting? I'm not sure how there can be infinitely many solutions? Any help would be appreciated!

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Algebraic solution is best, graphing can be dicey.
First one, substitute, it's ready to go.
Substitute the second eq. into the first and solve for x.

Then use the second eq. to get y.

(-2,-4)
Since you get one unique solution the system is consistent and independent.
.
.
.
Second one.
If you look at the second eq. it's the first eq. multiplied by 3.
They're the same equation.
If you graphed them, they'd be the same line.
It is a dependent system.
Every solution of the first equation is also a solution of the second equation so there are infinitely many solutions.

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