Question 362348: How do you know when an equation has infinetly many solutions, and when an equation has no solution?
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! When your equations lead to an inconsistency, such as,  or similar, then you have two parallel lines with no solution.
Example:
1.
2.
Subtract eq. 2 from eq. 1,
No solution, the lines are parallel.
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When your equations lead to an identity, such as,  or similar, then you have two lines that are the same line and have infinitely many solutions.
1.
2.
Multiply eq. 1 by -2 and add to eq. 1,
The lines are the same line (eq. 2 is 2 times eq. 1), there are infinitely many solutions (every solution of eq. 1 is also a solution of eq. 2).
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