2D - Simultaneous linear equations
2D - Content video: Solving simultaneous linear equations
This video covers the theory and several examples relating to how to solve simultaneous linear equations.
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Introduction to simultaneous linear equations:
A set of simultaneous linear equations involves two, or more, linear relationships. For example: \(y=2x+1\) and \(x+y=4\).
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How many solutions?
When solving two linear equations simultaneously it is possible to have no solutions, one solution or infinitely many solutions.
When solving two linear equations simultaneously it is possible to have no solutions, one solution or infinitely many solutions.
No solutions:
This occurs when two linear equations are parallel, but are not the same line.
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One solution:
This occurs when the two linear equations are non-parallel.
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Infinitely many solutions:
This occurs when the two lines are exactly the same.
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2D - Example 1: Solving simultaneous linear equations using substitution and elimination
Solve the following pair of simultaneous equations using substitution and then using elimination.
(1) \(2x+y=3\) (2) \(x+4y=-2\) |
2D - Example 1: Video solution
2D - Example 1: Practice
Question 1: ABC Question 2: ABC 2D - Example 1: Solutions
Question 1: ABC Question 2: ABC |
2D - Example 2: The number of solutions to simultaneous linear EQUATIONS
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2D - Example 2: Video solution
2D - Example 2: Practice
Question 1: ABC Question 2: ABC 2D - Example 2: Solutions
Question 1: ABC Question 2: ABC |
2D - Example 3: Worded questions involving simultaneous linear equations
Consider two numbers, \(a\) and \(b\), where four times a number plus three times the other is equal to 61 and the sum of the two numbers is 17.
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2D - Example 3: Video solution
2D - Example 3: Practice
Question 1: ABC Question 2: ABC 2D - Example 3: Solutions
Question 1: ABC Question 2: ABC |
2D - Example 4: Worded questions involving simultaneous linear equations (CAS)
At a particular shop James buys 2 pies and 5 soft drinks for $25.00. At the same shop, Jane buys 3 pies and 3 soft drinks for $23.10.
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2D - Example 4: Video solution
2D - Example 4: Practice
Question 1: ABC Question 2: ABC 2D - Example 4: Solutions
Question 1: ABC Question 2: ABC |