Unformatted text preview: 2 + (y − 1)2 = 2, which is
√
a circle centered at (1, 1) with a radius of 2. Choosing (1, 1) to represent the inside of the
circle, (1, 3) as a point outside of the circle and (0, 0) as a point on the circle, we ﬁnd that
the solution to the inequality is the inside of the circle, including the circle itself. Our ﬁnal
answer, then, consists of the points on or outside of the circle x2 + y 2 = 4 which lie on or
inside the circle (x − 1)2 + (y − 1)2 = 2. To produce the most accurate graph, we need to ﬁnd
where these circles intersect. To that end, we solve the system
(E 1)
x2 + y 2 = 4
2 − 2x + y 2 − 2y = 0
(E 2) x 8.7 Systems of NonLinear Equations and Inequalities 543 We can eliminate both the x2 and y 2 by replacing E 2 with −E 1 + E 2. Doing so produces
−2x − 2y = −4. Solving this for y , we get y = 2 − x. Substituting this into E 1 gives
x2 + (2 − x)2 = 4 which simpliﬁes to x2 + 4 − 4x + x2 = 4 or 2x2 − 4x = 0. Factoring yields
2x(x − 2) which gives x = 0 or x = 2. Substituting these values into y = 2 − x gives the
points (0, 2) and (2, 0). The intermediate graphs and ﬁna...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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