To find the value of 2 quantities x and y, we need to use 2 different equations that relate the unknowns to each other. Such equations are usually referred to as simultaneous equations.

The image at the top of the page shows a graph of both
2x + y = 4 and 6x - 3y = 0. The 2 lines clearly meet at the co-ordinates (1,2) and so x = 1,
y = 2 is the solution that satisfies both these equations.

In industrial processes, engineers often have to work with a large number of equations, each linking the unknown quantities together.

Before proceeding, you need to understand what is meant by the term coefficient. This is simply the number preceeding the variable.
So, in the second equation above, the coefficient of x is 6 and the coefficient of y is -3.

Unit 7.1: Modelling using simultaneous equations.

Unit 7.2: The addition and subtraction method.

Unit 7.2.1: Multiplication of one or both equations.

*Unit 7.2.2: Simultaneous equations with fractions.

Unit 7.3: The substitution method.

*Unit 7.3.1: Three simultaneous equations.

*Unit 7.4: Tackling equations where one equation is non-linear.

Unit 7.5: Real-life applications at the Esso Petroleum Company.

Learning Objectives
In this section the student will be able to

• Solve simultaneous linear equations via elimination of one of the variables.
• Solve simultaneous linear equations via the addition/ subtraction method.
• Recognise how real-life problems can be modelled by simultaneous equations.
• Solve simultaneous equations where one of the equations is non-linear.

* difficult work

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