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 -5-137

And for the line y = 3 - x:
  x   -1  0  1  2 
 y 4321

Plot both lines on the same axes. Part of the graph is shown below.

Graphs of both lines

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 = 0.8
y = 2.2

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