GCSE: Simultaneous equations: Part 1

Solving them algebraically

This particular section requires a fairly sound knowledge of solving linear equations.

To understand the geometrical interpretation, go to the section on ‘Simultaneous equations graphically’

The solutions to these equations are positive, integers (whole numbers). Part 2 will go on to develop skills involving fractions and negative solutions

Contents

1)           Solving linear simultaneous equations with positive coefficients

2)          Solving linear simultaneous equations with negative coefficients

3)          Solving linear simultaneous equations  which require you to pre-multiply at least one of the equations

Solving linear simultaneous equations   becomes   The solution is therefore Observe what happens if we do .   Now substitute    becomes      So the solution is: If we do    Substitute into (2)  So, becomes   The solution is therefore This time, if we do    Substitute into   So, becomes     The solution is therefore This time, if we do    Substitute into Sometimes we need to pre-multiply one of the equations first.    So, becomes   The solution is therefore The coefficients of the y in both equations do not match. So we pre-multiply the whole of equation by 2 and call this new equation . We keep equation the same     We now do    Substitute into     So, becomes    The solution is therefore The coefficients of the y in both equations do not match. So we pre-multiply the whole of equation by 5 and call this new equation . Also we pre-multiply the whole of equation by 2 and call this new equation .   We now do    Substitute into 