Simultaneous Equations

 

 

 

Contents

 

Introduction

 

Elimination Method

 

Substitution Method

 

Linear and non-linear equations 

 

Problem Solving

 

Quiz 

 

 

Algebra Main Page

 

Simultaneous Equations

What are Simultaneous Equations?

Let say you are given a problem:

Seven cups of tea and 4 pieces of cake cost $5.30 while 5 cups of tea and 2 pieces of cake cost $3.40. Find the cost of one cup of tea and a piece of cake.

If you put it in equation form, it will look like this:

7t + 4c = $5.30

 5t + 2c = $3.40, 
where t represents tea and c represents cake
 
You can draw up a table of values for 7t + 4c and 5t + 2c using different values for t and c.
 
t 0.35 0.40 0.50 0.60 0.70 1.00
c 0.80 1.00 0.45 0.90 0.50 2.00
7t + 4c 5.65 6.80 5.30 7.80 6.90 15.00
5t + 2c 3.35 4.00 3.40 4.80 4.50 9.00
 
You will find that there is a pair of values of t and c that satisfies both equations. This particular pair, t=$0.50 and c=$0.45, satisfies the two equations simultaneously.
 
We say that t=$0.50 and c=$0.45 is the solution to the simultaneous linear equations 7t + 4c = $5.30 and 5t + 2c = $3.40
 
Thus, to solve a linear equation with two unknowns, two different equations are needed. Similarly, to solve a linear equation with three unknowns, three different equations are needed and so on.
 
 
What are the methods used?
 
There are three common methods of solving simultaneous equations. We shall introduce two methods here: the elimination method and substitution method. The third method, the graphical solution method, will be dealt with in curve sketching.
 
 
Why learn Simultaneous Equations?
 
Simultaneous Equations can be used to solve problems like the one mentioned above. It is a better method to use than trial and error, as it is more reliable, simpler and faster.