# Simultaneous Equations (Mathematics Lesson)

# What Are Simultaneous Equations?

A simultaneous equation is a set or system of equations containing multiple variables which has a solution that simultaneously satisfies all of the equationsFor example, the set of simultaneous linear equations:

has a solution x = 1, y = 2.

**Note**: The letters - x and y - are called variables or unknowns.

The numbers in front of them are called co-efficients. Equation (1) is: (2 × x) + (1 × y) = 4.

# Real Examples of Simultaneous Equations

An example of 2 simultaneous equations with 2 unknowns is:The solution to these simultaneous equations is x = 1, y = 5.

An example of 3 simultaneous equations with 3 unknowns is:

The solution to these simultaneous equations is x = 2, y = 3, z = 4.

# How to Solve Simultaneous Equations

To solve simultaneous equations, use:##### Curriculum

##### Quick Test

**show**

##### Note

**WHAT'S IN A NAME?**

Simultaneous equations are so called because the solution solves all the equations at the same time, or simultaneously.

# VARIABLES AND UNKNOWNS

The x and y in the simltaneous equations are called variables or unknowns.They each have a value which solves all the simultanous equations.

The simultaneous equations must have the same variables as each other for them to be simultaneous equations. For example:

are not simultaneous equations.

**NUMBER OF UNKNOWNS = NUMBER OF EQUATIONS**

In the simultaneous equations shown to the left, there are 2 equations and 2 unknowns (x and y).

In general, to solve simultaneous equations, there must be as many independent equations as there are unknowns.

If there were 3 unknowns (e.g. x, y, and z), 3 equations would be needed to solve them.