Page 162 - Mathematics

When solving linear simultaneous equations graphically, the graphs of the equations
are drawn on the same xy -plane.The coordinates of the point of intersection of the
lines is the solution of the system of equations. If the lines of the graphs drawn do
not meet or intersect, then the system of simultaneous equations have no solution.
In this case, the lines are said to be parallel.

Example 6.30

Determine graphically the solution of the following systems of simultaneous
equations.
Tanzania Institute of Education
x
y = 2x − 1 and y = −+ 2.
Solution

x
Given the two equations y = 2x − 1 and y = −+ 2. Construct the tables of
values of the two equations as follows.
x
Table of values for y = 2x − 1 Table of values for y = −+ 2
x − 1 0 1 2 x 1 − 0 1 2

y − 3 1 − 1 3 y 3 2 1 0

Use the set of ordered pairs in each table to draw the graph of each of the
equations on the same xy-plane and identify a point of intersection. Label
each graph by its corresponding equation.

y

3
y = 2x - 1

2

1 (1, 1)
y = -x + 2 x

1
3
0
Mathematics Form One From the graph, the two lines intersect at the point (1, 1).
2
-1
-1

1
Therefore, x = and y = is the solution of the system of simultaneous
1
equations.

156

25/10/2024 09:52:03
Mathematics form 1.indd 156 25/10/2024 09:52:03
Mathematics form 1.indd 156