Unformatted text preview: ns. In fact, while we characterize systems of nonlinear equations as
being ‘consistent’ or ‘inconsistent,’ we generally don’t use the labels ‘dependent’ or ‘independent’.
Secondly, as we saw with number 4, sometimes making a quick sketch of the problem situation can
save a lot of time and eﬀort. While in general the curves in a system of non-linear equations may
not be easily visualized, it sometimes pays to take advantage when they are. Our next example
provides some considerable review of many of the topics introduced in this text.
Example 8.7.2. Solve the following systems of equations. Verify your answers algebraically
graphically, as appropriate. y + 4e2x = 1
z (x − 2) =
x2 + 2xy − 16 = 0 2.
y 2 + 2ex = 1
y 2 + 2xy − 16 = 0
3. 2 + y2 =
(x − 2) and
1. At ﬁrst glance, it doesn’t appear as though elimination will do us any good since it’s clear
that we cannot completely eliminate one of the variables. The alternative, solving...
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