There are several ways of solving simultaneous equations. You should know when and how to use each method.

You are shown the elimination and more general substitution methods.

 

Elimination method

When the two equations have the same format then either the x terms or the y terms are eliminated by subtracting or adding the two equations together. In the first example the x terms are both the same, (3x). You are shown how to solve this type but you may wish to try it first as part of your maths revision before looking at the worked solution.

• Tutorial and worked solution to (1)

 

In the next example I have changed the y terms to a minus sign. You need to be careful in these types.

• Tutorial and worked example to (2)

 

In the next example I have made the y terms the same instead of the x terms, both -5y.

• Tutorial and worked example to (3)

 

It maybe that the y terms are the same but have different signs. You must approach this differently.

• Tutorial and worked solution to (4)

 

Now we look at equations where the x terms and the y terms are not the same. Two ways of doing this are shown.

• Tutorial and worked solution to (5) by eliminating the x terms
• Tutorial and worked solution to (5) by eliminating the y terms

 

Substitution method

In equations that do not have similar formats or contain terms in x², y² or xy you will need to use the substitution method. In the examples that follow, I show you how to do this and how the solutions relate to the intersection of the two graphs. Again you may wish to try these first as part of your maths revision before looking at my worked solutions.

• Tutorial and worked solution to (6)

• Tutorial and worked solution to (7)

 

 

 

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