SOLUTION: When solving systems of linear equations,what is the difference between a "true statement that yields infinitely many solutions" and a "false statement that yields no solution"?

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Question 173224: When solving systems of linear equations,what is the difference between a "true statement that yields infinitely many solutions" and a "false statement that yields no solution"?
Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
A system of equations that produces the situation "there are no solutions" means that the graphs of the lines represented by the linear equations never intersect, the lines are parallel.
A system of equations that produces the situation "there are infinitely many solutions" means that the two are equations are really one and the same equation. The mathematical way of saying this is that the system is said to be dependent. One equation is a multiple of the other equation.