SOLUTION: what are the possible coordinates of a point where the line y=x-4 and the circle x^2+y^2=40 meet. thank you !!!!!

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Question 299715: what are the possible coordinates of a point where the line y=x-4 and the circle x^2+y^2=40 meet. thank you !!!!!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
what are the possible coordinates of a point where the line y=x-4 and the circle x^2+y^2=40 meet. thank you !!!!!

 

Here's how to find those points algebraically:

system%28y=x-4%2Cx%5E2%2By%5E2=40%29

Substitute %28x-4%29 for y in the second equation:

x%5E2%2By%5E2=40
x%5E2%2B%28x-4%29%5E2=40
x%5E2%2B%28x-4%29%28x-4%29=40
x%5E2%2Bx%5E2-4x-4x%2B16=40
2x%5E2-8x%2B16=40
2x%5E2-8x-24=0
x%5E2-4x-12=0
%28x-6%29%28x%2B2%29=0
matrix%282%2C2%2C%0D%0A%22x-6=0%22%2C%22x%2B2=0%22%2C%0D%0A%22x=6%22%2C++++%22x=-2%22%29

Substitute 6 for x in y=x-4

y=x-4
y=6-4
y=2

So one point is (x,y) = (6,2)

Substitute -2 for x in y=x-4

y=x-4
y=-2-4
y=-6

So the other point is (x,y) = (-2,-6)

Edwin