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**Unformatted text preview: **10
10
1
x
=− + 2
+2
5 + 2 x3 + x
x
x
x + 1 (x + 1)2 (k) 4x3 − 9x2 + 12x + 12
1
4
3x + 1
=
+
+2
x4 − 4x3 + 8x2 − 16x + 16
x − 2 (x − 2)2
x +4 (l) 2x2 + 3x + 14
1
1
=2
+
(x2 + 2x + 9)(x2 + x + 5)
x + 2 x + 9 x2 + x + 5 531 532 8.7 Systems of Equations and Matrices Systems of Non-Linear Equations and Inequalities In this section, we study systems of non-linear equations and inequalities. Unlike the systems of
linear equations for which we have developed several algorithmic solution techniques, there is no
general algorithm to solve systems of non-linear equations. Moreover, all of the usual hazards of
non-linear equations like extraneous solutions and unusual function domains are once again present.
Along with the tried and true techniques of substitution and elimination, we shall often need equal
parts tenacity and ingenuity to see a problem through to the end. You may ﬁnd it necessary to
review topics throughout the text which pertain to solving equations involving the various functions
we have studied thus far. To get the section rolling we begin with a fairly routine example.
Example 8.7.1. Solve the following systems of equations. Verify your answers algebraically and
graphically.
1. x2 + y 2 = 4
4x2 + 9y 2 = 36 3. x2 + y 2 = 4
y − 2x...

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