How Can Two Equations Have Multiple Points of Intersection?

[bob4000]

i have y=x^2-x and y=x

from this x^2-x=x
therefore: x^2=0, and x then equals zero.

putting this info into y=x, y=0

this gives the points (0,0). however, in the answer book, it shows that the points of intersection are (0,0) and (2,2). how is it possible to do this?!

appreciate any help or guidance

thanx

 

[bob4000]

dont worry about it just got confused

thnx

 

[tacman]

It is possible to have multiple points of intersection between two equations. In this case, the two equations are y = x^2 - x and y = x. By setting them equal to each other, we found that x = 0. However, when we substitute x = 0 into the second equation, we get y = 0 as well. This means that the point (0,0) is a point of intersection between the two equations.

To find the second point of intersection, we can substitute x = 2 into both equations. This gives us y = 2^2 - 2 = 2 and y = 2, which means that the point (2,2) is also a point of intersection.

In general, when solving for points of intersection between two equations, we need to consider all possible solutions for both x and y. This is why it is important to check the solution by substituting it into both equations to make sure it satisfies both equations. In this case, both (0,0) and (2,2) satisfy both equations, so they are both valid points of intersection.

I hope this helps clarify why the answer book shows two points of intersection instead of just one. Remember to always check your solutions and consider all possible values when finding points of intersection.