SIMULTANEOUS LINEAR EQUATIONS

CONTENT

1. Graphs of Linear Equations (Revision)
2. The Concept of Simultaneous Equations
3. Compilations of Tables of Values
4. Graphical Solution of Simultaneous Linear Equations in Two Variables

Graphs of Linear Equations (Revision)

For any value of \(x\) there is a corresponding value of \(y\). \(x\) is called the independent variable. Values of x are given on the horizontal axis. \(y\) is called the dependent variable. Values of \(y\) are given on the vertical axis. The graph of a linear equation is always a straight line. Thus it is sufficient to plot only two points to be able to draw the line. In practice it is better to plot three points or more. If it lies in a straight line, your working is probably correct.

Example 1:

Draw the graph of \(y = x + 1\) for values of \(x\) from 0 to 3.

Solution:

When \(x = 0\), \(y = 0 + 1 = 1\)

When \(x = 1\), \(y = 1 + 1 = 2\)

When \(x = 2\), \(y = 2 + 1 = 3\)

When \(x = 3\), \(y = 3 + 1 = 4\)

\(y = x + 1\)

Using a scale of 2cm = 1 unit for both axes, we plot a graph of \(y\) against \(x\) for the equations.