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__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 |