Modelling and control by Anthony Rossiter

SIMULTANEOUS EQUATIONS AND STRAIGHT LINES

 

These videos give an introduction to straight lines. Where do they come from and, for example, what does the formulation y=mx+c represent?

Having understood what a straight line represents, the videos move onto concepts of simultaneous equations, that is, when two straight lines meet. The videos begin by giving simple everyday examples of scenarios where straight lines occur and where the intersection is meaningful.

Finally, the videos introduce simple techniques for solving for the intersection points, again focussing on commonsense approaches rather than abstract concepts. Use the left hand toolbar to access the other chapters and themes.

It is implicit that for many engineering topics, students have core competence in some mathematical topics such as polynomials, roots, complex numbers, exponentials, logarithms and Laplace.

This section contains the following topics. Under each topic there are hardcopy (pdf) notes, a video talk through of key derivations with example problems and also a tutorial sheet for users to test themselves.

  1. Simultaneous equations 1 - what is a straight line?
  2. Simultaneous equations 2 - equation of a straight line in everyday terms.
  3. Simultaneous equations 3 - algebraic formulae for a straight line.
  4. Simultaneous equations 4 - intercepts of straight lines.
  5. Simultaneous equations 5 - simple solution method.
  6. Simultaneous equations 6 - tutorial sheet.
  7. Simultaneous equations 7 - methods used in schools.

Simultaneous equations 1 - what is a straight line

Introduction to simple scenarios which can be described by a straight line equation.

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Simultaneous equations 2 - equation of a straight line in everyday terms

Introduces the concept of straight lines using everyday scenarios which are easy to relate to. Introduces concepts of gradient and intercept with the vertical axis, again in terms of everyday scenarios.

Quick test question

In the standard equation y = mx +c, which of the following is true?
A. m represents the intercept with the y-axis.
B. m represents the normal.
C. c represents the intercept with the y-axis.
D. None of the above.

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Simultaneous equations 3 - algebraic formulae for a straight line

Develops video 2 by introducing the concept of 'abstract' variables to represent the terms in a straight line and hence the general equation form of 'y=mx+c'.

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Simultaneous equations 4 - intercepts of straight lines

Use a number of everyday scenarios to explain the meaning and importance of simultaneous equations and the intercept point.

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Simultaneous equations 5 - simple solution method

Gives a simple everyday interpretation of simultaneous equations from which the video demonstrates a solution method which is simple and intuitive with minimal reliance on abstract mathematics.

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Simultaneous equations 6 - tutorial sheet

Gives a number of worked examples of solving simultaneous equations. Students can pause the video and try the examples themselves before watching the solutions.

Quick test question

A simple way of solving simultaneous equations is to:
A. Sketch both lines and find the intercept.
B. Subtract one equation from the other.
C. Keep guessing different pairs of values until you find some that work.
D. None of the above.

Simultaneous equations 7 - methods used in schools

This video introduces the algebraic methods used in school to solve simultaneous equations. It is shown that this method is in fact equivalent to he intutive method of earlier videos (and thus in fact could be avoided where students struggle with its abstract nature).

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