SOLUTION: How do you identify whether the graph of a system of linear equations would be two intersecting lines, two distinct parallel lines, or two coincident lines?

Question 577199: How do you identify whether the graph of a system of linear equations would be two intersecting lines, two distinct parallel lines, or two coincident lines?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
All you have to do is look at the slope.
If the equations are not already in this form:
, then put them into that form.
Look at for each equation.
is the slope of each.
Cases:
(1) is the same for all, but all the
's are different
These are all parallel lines
---------------------
(2) is the same for all, and
is the same for all.
These lines are coincident
---------------------
(3) is different for all the lines
( It doesn't matter what is )
All these lines intersect each other
None are coincident and
none are parallel
----------------
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