The terms simultaneous equations and systems of equations refer to conditions where two or more unknown variables are related to each other through an equal number of equations.

In this video you will see the easy steps to solve simultaneous equations using elimination method.

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**Video length: 2min 57sec**

**Category: Maths videos**

**NOTE: **The method is not quite as hard as it first seems, but it helps if you know why it works.

It works because of two properties of equations:

- Multiplying (or dividing) the expression on each side by the same number does not alter the equation.
- Adding two equations produces another valid equation:

e.g. 2x = x + 10 (x = 10) and x − 3 = 7 (x also = 10).

Adding the equations gives 2x + x − 3 = x + 10 + 7 (x also = 10).

The object is to manipulate the two equations so that, when combined, either the x term or the y term is eliminated (hence the name) − the resulting equation with just one unknown can then be solved:

Here we will manipulate one of the equations so that when it is combined with the other equation either the x or y terms will drop out. In this example the x term will drop out giving a solution for y. This is then substituted into one of the original equations.

Label your equations so you know which one your are working with at each stage.

Equation [1] is 2y + x = 8

Equation [2] is 1 + y = 2x

Rearrange one equation so it is similar to the other.

[2] y – 2x = -1

also 2 x [1] gives 4y + 2x = 16 which we call [3]

[2] y – 2x = -1

[3] 4y +2x = 16

[2] + [3] gives 5y = 15

so y = 3

substituting y = 3 into [1] gives 1 + (3) = 2x

so 2x = 4, giving x = 2 and y = 3

**Exercises**

Solve the following using elimination method.

a.

- x - 5y = 7.
- 2x -4y = 8.

- 2x + 4y = 12.
- x + 8y = 30.

- 2x - 4y = 10.
- -4x+5y = -26.

- 6x + 2y = 10.
- 10x - 3y = 12.

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