Simultaneous Equations

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Description of Levels

Projectable - A set of simultaneous equations designed to be shown one at a time to the whole class.

Level 1 - Equations that can be added or subtracted to eliminate one variable.

Level 2 - Equations that can be added or subtracted to eliminate one variable after one of the equations has been multiplied by a constant.

Level 3 - Equations that can be added or subtracted to eliminate one variable after both of the equations have been multiplied by constants.

Level 4 - Equations with two variables that are not written in the standard way.

Level 5 - Real life problems that can be solved by writing them as simultaneous equations.

Level 6 - Equations which include fractions in some way.

Level 7 - Linear, quadratic and other pairs of simultaneous equations.

These Level 7 questions will require you to be able to solve Quadratic Equations.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Simultaneous Equations including lesson Starters, visual aids, investigations and self-marking exercises.

Extension

There is a printable worksheet to go with this activity. It is an exercise that appeared in an algebra book published in 1895. It starts with basic questions but soon gets tricky!

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help Video

The examples used in the video are available to teachers as projectable slides.

Level 5 Example

What two numbers add up to 50 and have a difference of 12?

Let the smaller number be \(x\) and the larger number be \(y\).

\(y+x=50 \qquad \mathbf{A}\\y-x=12 \qquad \mathbf{B} \)

Add equation \( \mathbf{A} \) to equation \( \mathbf{B} \)

\(2y=62\)
\(y=31\)

Substitute this value for \(y\) into equation \( \mathbf{A} \).

\(31+x=50\)
\(x=19\)

The simultaneous equations have been solved.
The smaller number is 19 and the larger number is 31.

You can check your answers by substituting them both into equation \( \mathbf{B} \) to see if it balances.

This example is not intended to teach you everything you need to know about this type of simultaneous equations. It is here as a reminder and is no substitute for your teacher or tutor.