
- •Solving a linear equation
- •Checking solutions
- •What are simultaneous equations?
- •How to solve 2 simultaneous equations
- •Elimination
- •Elimination method 1
- •Elimination method 1
- •Elimination method 2
- •Elimination rules for method 2
- •Elimination rules for method 2
- •Elimination rules for method 2
- •Practice

Simultaneous Linear Equations
What they are and how to work with them
Steve Sugden
Bond University
10 May 2011
Steve Sugden (Bond University) |
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10 May 2011 |
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Solving a linear equation
Tony bought two cans of the same soft drink and received change of $4 from $10.
What is the cost of one can of soft drink?
This problem may be expressed as a linear equation in one unknown.
If we let the cost of one can be $x then we have 2x + 4 = 10
To solve it we can use elementary algebra:
2x + 4 |
= |
10 |
(Subtract 4) |
2x |
= |
10 4 |
(Simplify) |
2x |
= |
6 |
(Divide by 2) |
x |
= |
3 |
(Solution) |
We just solved one equation in one unknown.
It is important to check this solution.
Steve Sugden (Bond University) |
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10 May 2011 |
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Checking solutions
There are at least two types of checking. For an abstract problem, you should always perform the …rst one; for a "word problem", you should do both. Here they are:
Check #1: Substitute the value found back into the original equation and verify that it "works".
Check #2: Interpret the solution in terms of the original word problem to see if it makes sense.
If any check fails then you need to do some detective work to …nd any ‡aws and …x them.
This takes practice.
Problem
Do these checks for the soft drink example.
Steve Sugden (Bond University) |
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10 May 2011 |
3 / 13 |

What are simultaneous equations?
These are two (or more) equations in two (or more) unknowns and occur very often in practical problems.
Example
Two people bought quantities of the same two items. Anne bought 4 biros and 3 rulers for $23. Bob bought 3 biros and 5 rulers for $29. What does each item cost? This problem (a so-called "word problem") can be formulated as two simultaneous equations. We suppose a biro costs $b and a ruler costs $r. Then:
4b + 3r |
= |
23 |
2b + 5r |
= |
29 |
Steve Sugden (Bond University) |
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10 May 2011 |
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How to solve 2 simultaneous equations
Solving 2 simultaneous linear equations
4b + 3r |
= |
23 |
2b + 5r |
= |
29 |
To solve this pair of equations we need a strategy, beyond what we used for just one equation.
Strategy: try to transform it to one like we just solved, i.e., with just one unknown.
Note: this is a general principle of problem-solving: try to reduce a new problem to one which you already know how to solve.
Steve Sugden (Bond University) |
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10 May 2011 |
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