**Unformatted text preview: **1 for x, we get x = y 2 − 4. Substituting this into E 2 gives y = y 2 − 4 − 2, or
y 2 − y − 6 = 0. We ﬁnd y = −2 and y = 3 and since x = y 2 − 4, we get that the graphs
intersect at (0, −2) and (5, 3). Putting all of this together, we get our ﬁnal answer below.
y y y 3 x −5 4
− −3 y2 − 4 ≤ x 2 3 4 5 x −3 x<y+2 −5 4
− 2 3 4 5 x −3 y2 − 4 ≤ x < y + 2 2. To solve this system of inequalities, we need to ﬁnd all of the points (x, y ) which satisfy
both inequalities. To do this, we solve each inequality separately and take the set theoretic
intersection of the solution sets. We begin with the inequality x2 + y 2 ≥ 4 which we rewrite as
x2 + y 2 − 4 ≥ 0. The points which satisfy x2 + y 2 − 4 = 0 form our friendly circle x2 + y 2 = 4.
Using test points (0, 0) and (0, 3) we ﬁnd that our solution comprises the region outside the
circle. As far as the circle itself, the point (0, 2) satisﬁes the inequality, so the circle itself
is part of the solution set. Moving to the inequality x2 − 2x + y 2 − 2y ≤ 0, we start with
x2 − 2x + y 2 − 2y = 0. Completing the squares, we obtain (x − 1)...

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