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Question 193437: what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x?
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They mean for you to find x/y pairs that make both equations true.
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Substitute y = 2-x in the other equation to solve for "x":
x^2 + (2-x)^2 = 100
x^2 + 4 -4x + x^2 = 100
2x^2-4x-96 = 0
x^2 -2x-48 = 0
(x-8)(x+6) = 0
x = 8 or x = -6
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If x = 8, y = 2-x = 6 giving you point (8,6)
If x = -6, y = 2-x = 9 giving you point (-6,8)
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Cheers,
Stan H.
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