Sometimes you will be asked to find 2 unknown values by solving 2 equations at the same time. These types of equations are called **simultaneous equations**.

Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.

The first step is to try to eliminate one of the unknowns.

Solve these simultaneous equations and find the values of **x** and **y**.

- Equation 1: 2x + y = 7
- Equation 2: 3x - y = 8

Add the two equations to eliminate the **y**s:

- 2x + y = 7
- 3x - y = 8
- ------------
- 5x = 15
- x = 3

- Now you can put x = 3 in either of the equations.
- Substitute x = 3 into the equation 2x + y = 7:
- 6 + y = 7
- y = 1

So the answers are **x = 3** and **y = 1**

Sometimes you will need to multiply one of the equations before you can add or subtract. Have a look at the activity below.

On other occasions you will need to multiply both equations to find the unknown values. Always look for a way to cancel out one of the unknown terms. Have a go at the question below.

- Question
- Solve the two equations:
- Equation 1: 2a - 5b = 11
- Equation 2: 3a + 2b = 7

- Answer
- 4a - 10b = 22 (Multiply by 2)
- 15a + 10b = 35 (Multiply by 5)
- ----------------------
- 19a = 57 (Adding)
- a = 3

- Put a = 3 into the equation 3a + 2b = 7:
- 9 + 2b = 7
- 2b = -2
- b = -1

So the answers are

**a = 3**and**b = -1.**

We can also use a method of substitution. Look at the following example:

Solve the simultaneous equations:

Equation 1: y - 2x = 1

Equation 2: 2y - 3x = 5

Rearranging Equation 1, we get y = 1 + 2x

We can replace the 'y' in equation 2 by substituting it with 1 + 2x

Equation 2 becomes: 2(1 + 2x) - 3x = 5

2 + 4x - 3x = 5

2 + x = 5

x = 3

Substituting x = 3 into Equation 1 gives us y - 6 = 1, so y = 7.

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

**This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.**