Unformatted text preview: e early stages of the problem. Not only does this promote uniformity in the units,
it also serves as a quick means to check if an equation makes sense.6
We close this section discussing how non-linear inequalities can be used to describe regions in
the plane which we ﬁrst introduced in Section 2.4. Before we embark on some examples, a little
motivation is in order. Suppose we wish to solve x2 < 4 − y 2 . If we mimic the algorithms for solving
nonlinear inequalities in one variable, we would gather all of the terms on one side and leave a 0
6 Carl would much rather spend his time writing open-source mathematics than gardening anyway.
In other words, make sure you don’t try to add apples to oranges! 8.7 Systems of Non-Linear Equations and Inequalities 541 on the other to obtain x2 + y 2 − 4 < 0. Then we would ﬁnd the zeros of the left hand side, that
is, where is x2 + y 2 − 4 = 0, or x2 + y 2 = 4. Instead of obtaining a few numbers which divide the
real number line into intervals, we get an equation of a curve, in this case, a circle, which divides
the plane into two regions - the ‘inside’ and ‘outs...
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