1 / 9

Conic Sections

Chapter 10. Conic Sections. 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. Nonlinear Systems of Equations and Their Applications. § 10.4. Nonlinear System of Equations.

ksanders
Télécharger la présentation

Conic Sections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  3. Nonlinear Systems of Equations and Their Applications § 10.4

  4. Nonlinear System of Equations 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. continued

  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. continued

  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

More Related