Simultaneous Equations (Mathematics Lesson)
What Are Simultaneous Equations?Simultaneous equations are a set of equations containing several variables which have a solution that simultaneously satisfies all of the equations.
For 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 EquationsAn 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 EquationsTo solve simultaneous equations, use:
NoteWHAT'S IN A NAME?
Simultaneous equations are so called because the solution solves all the equations at the same time, or simultaneously.
VARIABLES AND UNKNOWNSThe 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.