Showing posts with label substitution. Show all posts
Showing posts with label substitution. 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.

 

 

 

 

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Saturday, March 23, 2013

Elementary Algebra Exam #2

Click on the 10 question exam covering topics in chapters 3 and 4. Give yourself one hour to try all of the problems and then come back and check your answers.


Graph. Also, find and label both the x- and y-intercepts.
 
Are the following lines parallel, perpendicular, or neither? Justify your answer.
 

Find the equation of the line:
 
 

  

 9. A light aircraft, flying with the wind, can travel 270 miles in 2 hours. On the return trip, flying against the same wind, the plane can only travel 210 miles in the same amount of time. What is the speed of the wind?
10. Marcia invested a total of 2,500 dollars in two separate accounts. One account earned 6% annual interest and the other earned 8%. If her total interest for the year was 167 dollars, then how much did she invest in each account?
 
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