Year 10 Interactive Maths - Second Edition

## Solution of Linear Simultaneous Equations

There are many situations in which scientists, mathematicians, engineers and others have to consider problems involving more than one variable.

Consider the following two equations which contain the unknowns x and y.

If we determine the values of x and y such that equations (1) and (2) hold true, then the two equations are called simultaneous equations as they are considered together.

Simultaneous equations are solved approximately using the graphical method or exactly using an algebraic method.

### The Graphical Method

The graphical solution of linear simultaneous equations is the point of intersection found by drawing the two linear equations on the same axes.

#### Example 1

Solve the following simultaneous equations graphically.

##### Solution:

The graphical solution of the simultaneous equations

is given by the point of intersection of the linear equations.

Consider x + y = 8.

x-intercept:
When y = 0, x = 8

y-intercept:
When x = 0, y = 8

Consider x – y = 2.

x-intercept:
When y = 0, x = 2

y-intercept:

The diagram shows that the lines intersect at the point (5, 3). So, the solution of the simultaneous equations is x = 5 and y = 3 or (5, 3).

###### Note:

Often the answer obtained with the graphical method is not exact.