Further Algebra: Simultaneous Equations Part 1


When we say simultaneous equations, it means we will be solving two different equations at the same time.

Each equation will have two unknown values, usually x and y and because there are two unknown values, it is important to have two equations to be able to get the answers we are looking for.

In this way, we will find the values of ‘x’ and ‘y’ that will satisfy both of the equations at the same time.

To solve simultaneous equations our main goal is to try and eliminate one of the variables by adding or subtracting the equations from each other.

However, there are times when we need to multiply both equations by different amounts, so that we can arrive at the same value for one of the coefficients of one of the variables.

Example 1

Solve the simultaneous equations

and 

Since the signs next to the ‘y’s are of different operation, we can simply add the two equations and the ‘y’s will disappear.

We will therefore be left with 7x’s is equal to 28. This can then be solved to get ‘x’ is equal to 4

For our calculation we will substitute it into the first equation and then solve for ‘y’ It will give us an answer of ‘y’ is equal to 2.