from the linear equation: x = 7y - 75
intersect the two relations,
x^2 + y^2 = 225
(7y-75)^2 + y^2 - 225 = 0
49y^2 - 1050y + 5625 + y^2 - 225 = 0
50y^2 - 1050y + 5400 = 0
divide by 50
y^2 - 21y + 108 = 0
(y - 12)(y - 9) = 0
y = 12 or y = 9
if y = 12, x = 9
if y = 9 , x = -12
the bridge meets the point at (9,12) and (-12,9)
verification by Wolfram:
http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%3D+225+%2C+x%E2%80%937y%3D%E2%80%9375+from+-15+to+15
A circular pond is modeled by the equation x^2+y^2= 225. A bridge over the pond is modeled by a segment of the equation x–7y=–75. What are the coordinates of the points where the bridge meets the edge of the pond?
Can you teach me how to do this?
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