Posted by barb on Thursday, August 5, 2010 at 12:04pm.
how do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

math116  Henry, Friday, August 6, 2010 at 7:47pm
The question of how many solutions,
if any,usually comes up when solving
2 equations simutaneously. First, we
need to define solution: The solution is the point where the two lines inter
sect. I F they do not INTERSECT, there
is no solution. Parallel lines do not
INTERSECT and have no solution. We
identify parallel lines by the fact that they have = slopes. But their
Yintercepts are different.
Now surpose 2 equations have = slopes AND = Yintercepts, Then, they repre
sent the same line and all points on
the line intersect.Therefore, we have an INFINITE number of solutions.
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