SOLUTION: How do you know when an equation has infinetly many solutions, and when an equation has no solution?

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.
.
.
.
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).

RELATED QUESTIONS
How do you know when an equation has an infinitely number of solutions or when an... (answered by rapaljer)

How do you know when an equation has no... (answered by stanbon)

How do you know when an equation has infinitely many solutions? How do you know when... (answered by nabla)

How do you know when an equation has infinitely many solutions? How do you know when an... (answered by stanbon)

How do you know when an equation has infinitely many solutions? How do you know when an... (answered by mangopeeler07)

How do you know when an equation has infinitely many solutions? How do you know when an... (answered by ilana)

How do you know when an equation has infinitely many solutions? How do you know when an (answered by stanbon)

How do you know when an equation has infinitely many solutions? How do you know when an... (answered by Edwin McCravy)

How do you know when an equation has infinitely many solutions? How do you know when an... (answered by CharlesG2)