1. Chapter 10
Conic Sections

2. Chapter Sections 10.1 – The Parabola and the Circle 10.2 – The Ellipse
10.3 – The Hyperbola
10.4 – Nonlinear Systems of Equations and Their Applications
Chapter 1 Outline

3. Nonlinear Systems of Equations and Their Applications
§ 10.4
Nonlinear Systems of Equations and Their Applications

4. Nonlinear System of Equations
A nonlinear system of equations is a system of equations in which at least one equation is not linear, that is, one whose graph is not a straight line.

5. Solve Nonlinear Systems Using Substitution
Example Solve the previous system of equations algebraically using the substitution method.
Solution We first solve the linear equation 3x + 4y = 0 for either x or y. We will solve for y.
continued

6. Solve Nonlinear Systems Using Substitution
Now we substitute for y in the equation x2 + y2 = 25 and solve for the remaining variable, x.
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7. Solve Nonlinear Systems Using Substitution
Next, we find the corresponding value of y for each value of x by substituting each value of x (one at a time) into the equation solved for y.
The solutions are (4, -3) and (-4, 3).

8. Solve Nonlinear Systems Using Addition
Example Solve the system of equations using the addition method.
Solution If we add the two equations, we will obtain one equation containing only one variable.
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9. Solve Nonlinear Systems Using Substitution
Now solve for the variable y by substituting x = ± 1 into either of the original equations.
x = 1
x = -1
The solutions are