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