Simultaneous Equations – GCSE Maths Revision and Worksheets

What you need to know:

We use the term ‘simultaneous equations’ to refer to a collection of equations that are all true at the same time and for the same values of x, y, or whatever other variables are chosen in the given problem.

Sometimes you are given the simultaneous equations, such as

2x - 3y = 12
3x + 4y = 8

and asked to solve them. However, sometimes they are presented as word problems, and you are expected to be able to write down a pair of simultaneous equations from the information given to you in the question. In either case, you should become familiar with the methods of solving by both elimination and substitution. You may well prefer one over the other but you should be comfortable with both. Always make sure that you find both solutions (in this case x and y).

You should also understand that equations like in the example above correspond to straight lines on a graph, and moreover the coordinates of where those straight lines cross is precisely the solutions to the simultaneous equations. You may be asked to draw these lines, and find an approximate solution to the problem by reading from your graph where the lines cross.

On the higher course, it is also possible that you be asked to solve quadratic simultaneous equations, for example:

x^2 + y^2 = 4
y = 3x - 2

In this, the elimination method no longer works, and you must opt for substitution. This time, there will be two answers for x, each with a corresponding y value, so make sure to find both pairs of solutions.