Question 935189: how do you get the intersecting point on a graph?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! There are times when we need to find the point(s) common to two graphs. In other words, both graphs pass through the same point, and we may need to find out that point of intersection.
We can look at both graphs and see that they intersect, and sometimes, we may even be able to approximate the point or points of intersection just by looking at the two graphs together.
Very often, though, we can use algebra to find the exact intersection point(s) of two graphs.
First, we need the equations of the graphs. Let’s look at an example to see how we might use algebra to find their intersection.
Find the intersection of the two lines:  and 
you find two points for both line and graph them:
for 
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for 
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graph them:
by looking at the two graphs together, we see that both line passing through point ( , )-that is what we SEE as their intersection point
but, we might use algebra to find their intersection exactly:
so, solve the system:
------------------since left side same, right sides must be same too
 ....solve for
find
so, their intersection is at point (,)
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