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

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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