SOLUTION: Hi I need help with this- How many solutions are there to the following system equations: • y= 6-x • y= x^2-6x+6

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Question 732660: Hi I need help with this- How many solutions are there to the following system equations:
• y= 6-x
• y= x^2-6x+6
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The system of equations system%28y=+6-x%2Cy=+x%5E2-6x%2B6%29 has 2 solutions.
Substituting 6-x for y in +y=+x%5E2-6x%2B6 you get
6-x=x%5E2-6x%2B6 --> -x=x%5E2-6x --> x%5E2-5x=0 --> x%28x-5%29=0
So the solutions are x=0 and x=5 , 2 solutions.
For x=0 , y=6-0 --> y=6 gives you point (0,6).
For x=5 , y=6-5 --> y=1 gives you point (5,1).
Those 2 points are the intersections of the straight line represented by the linear function y=6-x and the parabola represented by the quadratic function y=+x%5E2-6x%2B6
graph%28300%2C300%2C-5%2C10%2C-5%2C10%2C6-x%2Cx%5E2-6x%2B6%29