# math116

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how do you know when an equation has infinitely many solutions? How do you know when an equation has no solution?

• math116 -

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
Y-intercepts are different.

Now surpose 2 equations have = slopes AND = Y-intercepts, 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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