math116
posted by barb .
how do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

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.