Dear students,

For today, you will be learning how to solve simultaneous equations. This is similar to the linear equations type you did in Sec 1, except that there are now 2 equations and 2 unknowns to find. You may complete the homework part later in the afternoon or night. Remember to PRINT the form you will complete in step 3.

Objectives:

1. Solve simultaneous linear equations by the elimination method
2. Solve simultaneous linear equations by the substitution method
3. Form and solve simultaneous linear equations from given word problems


1. Concept Mastery (30 mins)

View the shockwave file to learn the concept of simultaneous equations and how to solve them. It works like powerpoint slides so click on it to move.



If you are unable to view the shockwave file, you need to download the shockwave player from http://get.adobe.com/shockwave/

Now that you have an idea of what simultaneous equations are like and how to solve them, let's go into the details. There are a few ways to solve the 2 equations. You will learn the Elimination method and the Substitution method today. Always remember that when you have 2 unknowns, you will need 2 different equations to solve and hence arriving at 2 solutions.

(a) Solving Simultaneous Equations by the Elimination method

In this method, you will seek to make the coefficients of one of the variables the same and proceed to eliminate one of the variables by adding or subtracting the 2 equations.

Here are 4 videos on examples on solving simultaneous equations using the elimination method. It is not necessary to view all 4 but as much as you need to grasp the method.


[URL: http://www.youtube.com/watch?v=XM7Q4Oj5OTc]


[URL: http://www.youtube.com/watch?v=_IiNqXPnHQI]


[URL: http://www.youtube.com/watch?v=SskHNSxZALA]


[URL: http://www.youtube.com/watch?v=Zzt7A9Kxjq4]

(b) Solving Simultaneous Equations by the Substitution method

In this method, you will seek to make one of the variables the subject of the equation and proceed to substitute it into the other equation.

Here are 4 videos on examples on solving simultaneous equations using the substitution method. It is not necessary to view all 4 but as much as you need to grasp the method.


[URL: http://www.youtube.com/watch?v=8ockWpx2KKI]


[URL: http://www.youtube.com/watch?v=it3vYdV_oyc


[URL: http://www.youtube.com/watch?v=6GegfpLnIgY]

*Note: You will not be asked to use a specific method to solve the equations. However, depending on how the question is given, one method may have its advantages over the other so you should know both.

2. Quiz (20 mins)

You will test your understanding of the concept by completing 2 quizzes online.

Quiz 1: http://quiz.econ.usyd.edu.au/mathquiz/sim-eqns/quiz1.php
Quiz 2: http://quiz.econ.usyd.edu.au/mathquiz/sim-eqns/quiz2.php
Quiz 3: http://quiz.econ.usyd.edu.au/mathquiz/sim-eqns/quiz3.php

3. Reflections (10 mins)

Complete the questions posed: http://spreadsheets.google.com/viewform?formkey=dER6ZTZsam5xTnZScjhnRVY3ckRMTHc6MA

4. Homework (to be completed in the afternoon)

Textbook Ch 5, Complete the exercises in Section 5.3 and 5.4 on foolscap. The textbook introduces the graphical method as well - you do not need to learn this for the online learning.


5. Enrichment (Optional)

For those who like the challenge, solve this question simultaneously:

3y - 5z = -13
2x + 3y = 17
x + 3z = 19

Post your solution in the discussion board on this page.