Chapter 19

Graphical solution of

equations

19.1 Graphical solution of

simultaneous equations

Linear simultaneous equationsin two unknowns may
be solved graphically by

(a) plotting the two straight lines on the same axes,

and

(b) noting their point of intersection.

The co-ordinates of the point of intersection give the
required solution.
Here are some worked problems to demonstrate the
graphical solution of simultaneous equations.

Problem 1. Solve graphically the simultaneous

equations

2 x−y= 4

x+y= 5

Rearranging each equation intoy=mx+cform gives

y= 2 x− 4

y=−x+ 5

Only three co-ordinates need be calculated for each
graph since both are straight lines.

x 0 1 2

y= 2 x− 4 − 4 − 2 0

x 0 1 2

y=−x+ 5 5 4 3

Each of the graphs is plotted as shown in Figure 19.1.

The point of intersection is at (3, 2) and since this is the

only point which lies simultaneously on both lines

thenx= 3 ,y= 2 is the solution of the simultaneous

equations.

24 23 22 211

1

2

3

4

5

y

y 52 x 15

y 52 x 24

234 x

21

22

23

24

0

Figure 19.1

Problem 2. Solve graphically the equations

1. 20 x+y= 1. 80

x− 5. 0 y= 8. 50

DOI: 10.1016/B978-1-85617-697-2.00019-3