SOLUTION: how do you find the point of intersection when given two y= formulas without graphing?

Question 7666: how do you find the point of intersection when given two y= formulas without graphing?
Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
If the y= formulas, as you call them, are y = f(x) (that is to say y in terms of x) you solve the equations to find an y and a x that satisfy both equations simultaneously. That (x, y) set is a point that lies on both lines. That is the intersection.
The thing to check is whether the two functions are actually two different lines and, if so, whether they are parallel or not. This is why knowing the slope and y-intercept is important.
If the lines have the same slope but different y-intercepts, they are parallel and there is not solution.
If the lines have the same slope and the same y-intercept, they coincide and there are an uncountable number of solutions.
If the lines have different slopes, they intersect and there is one solution.
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