Question 978096: Y=x^2-5x+15 y=-×+10 find solutions to the system of equations
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Y=x^2-5x+15. The first doesn't factor.
y=-×+10
Set them equal.
-x+10=x^2-5x+15
x^2-4x+5=0
x=(1/2)(4+/- sqrt (16-25)=2+/-(3i/2)
The two solutions are complex.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
In the first place,  is NOT the same thing as  , so, as written, your problem cannot be solved. However, presuming you simply made a typo and you really meant:
So if  and  , then it must be true that  , right?
Collect like terms, put the quadratic into standard form ( ), and then calculate the discriminant. If the discriminant is positive, you have two solutions and two points of intersection. In this case, calculate the roots, and substitute each of them back into either of the original equations to find the -values so that you can specifiy the ordered pairs that represent the two points. If the discriminant is zero, there is only one point of intersection. If the discriminant is negative, then the two graphs do not intersect and the the solution set of the system is the empty set.
John
My calculator said it, I believe it, that settles it
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