Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts

Tuesday, July 23, 2013

Solving Nonlinear Systems

In this guide, we have solved linear systems using three methods: by graphing, substitution, and elimination.  When solving nonlinear systems, we typically choose the substitution method, however, sometimes the other methods work just as well.  Remember that to solve a system of equations means to find the common points - if they exist. Given a system of equations consisting of a circle and a line then there can be three possibilities for solutions.  Remember that solutions to a system are ordered pairs (x, y). These will be the points where they intersect.
  
Solve the nonlinear systems.

 

  
Given a circle and a parabola there are five possibilities for solutions.
  
  
These nonlinear systems given algebraically might look like:
To find the points in common, we will usually use the substitution method. But, as in this case, the graphing and elimination method work just as well.

Solve.

 

 

Certainly there are many ways to solve these problems. Experiment with other methods and see if you obtain the same results.

Solve.

 

 

 

 

YouTube Videos:





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Wednesday, June 26, 2013

Distance and Midpoint Formulas

In this section we will review the distance and midpoint formulas.
Notice that the distance formula results in a real number and that the midpoint formula results in an ordered pair.

[ Interactive: Distance and Midpoint ]

Given two points find the distance and midpoint between them.
   

   
   
   
Video Lessons:
 
Use the distance and/or midpoint formulas to solve the following.

Example: If the diameter of a circle is defined by the two points (-3, 4) and (7, 4), find the center and radius of the circle. (Hint: diameter = 2r)
Example: Find the area of a circle given center (-3, 3) and point (3, 3) on the circle.
   
Video Examples on YouTube:





 
YouTube Example: Find the coordinates of an endpoint given the other endpoint and the midpoint.
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