# Chapter 6 Conic Sections by TgH1xH8

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• pg 1
```									       Chapter 6
Conic Sections
Section 6.4
Nonlinear Systems of Equations
Nonlinear Systems of Equations
• The graphs of the equations in a
nonlinear system of equations can
have no point of intersection or one
or more points of intersection.
• The coordinates of each point of
intersection represent a solution of
the system of equations.
• When no point of intersection
exists, the system of equations has
no real-number solution.
• We can solve nonlinear systems of
equations by using the substitution
or elimination method.
Example

• Solve the following system of equations:

x  y 9
2   2

2x  y  3
Example continued

• We use the substitution method.
First, we solve equation (2) for y.
Example continued
• Next, we substitute
y = 2x  3 in equation (1) and solve for x:
Example continued
• Now, we substitute these numbers for x in
equation (2) and solve for y.

• x=0                            x = 12 / 5
Example continued

Check: (0, 3)                                 • Visualizing the
x2  y 2  9               2x  y  3             Solution

0 3 9
2     3
2(0)  (3)  3
99                         33

 12 9 
Check:         , 
 5 5
x2  y 2  9       2x  y  3
 
12 2
5
    
9 2
5
9      2( 12 )  ( 9 )  3
5       5

99                       33
Example
• Solve the following system of equations:
xy = 4
3x + 2y = 10
Example continued

Solve xy = 4 for y.

Substitute into
3x + 2y = 10.
Example continued
• Use the quadratic formula to solve:
3x  10 x  8  0
2
Example continued
• Substitute values of x to find y.
3x + 2y = 10
• Visualizing the
Solution
x = 4/3            x = 2

The solutions are
Example
• Solve the system of equations:
5 x  2 y  13
2      2

3x  4 y  39
2      2
Example continued

• Solve by elimination.
Example continued
• Substituting x = 1 in equation (2) gives us:
x=1                            x = -1

• The possible solutions are
Example continued

All four pairs check,   • Visualizing the Solution
so they are the
solutions.

```
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