 # Simultaneous Equations

 From: Dominic Walsh Date: 2 September 1999 Subject: Simultaneous Equations Can you give me some guidance how to solve the simultaneous equations:      y = 4x - 1   and      y = 3 - x using a graphical method.

### Maths Help suggests:

Each of the equations can be represented by a straight line.

If you draw both straight lines on the same graph, you should find that they cross.
The point where they cross is on both straight lines, so the x and y co-ordinates will satisfy both equations.

In other words:

 The co-ordinates of the point where the lines cross gives the solution to the simultaneous equations

You could use a table to help you plot the line y = 4x - 1:
 x -1 0 1 2 y -5 -1 3 7

And for the line y = 3 - x:
 x -1 0 1 2 y 4 3 2 1

Plot both lines on the same axes. Part of the graph is shown below. If you draw an accurate graph you will discover that the lines cross at the point

( 0.8 , 2.2 )

So the solution to the simultaneous equations is:
 x = 0.8y = 2.2