| Two linear equations in two variables
are said to be simultaneous if they are considered at the same
time.
Solution of Linear Simultaneous Equations
Simultaneous equations are solved exactly either by the substitution method
or
the elimination method. An approximate solution can be found
by using the graphical method.
Substitution Method
To solve simultaneous equations, find the value of y in
terms of x (or vice versa) for one of the two equations and then
substitute this value into the other equation.
Example 1
Solve the following simultaneous equations by using the substitution
method:
Solution:
Label the equations as follows:
From (1) we have:
y = 3x
...(3)
Substituting y = 3x in (2) gives:
So, the solution is (2, 6).
The Graphical Method
The graphical solution of the simultaneous equations
is given by the point of intersection of the graphs.
Consider the graph of
It passes through the origin (0, 0) and the point (1, 3).
Consider the graph of x + y = 8.
x-intercept: When y = 0, x = 8.
y-intercept: When x = 0, y = 8.
The lines intersect at (2, 6). So, the solution is (2, 6) as
shown in the diagram.
Note:
Often the answer obtained with the graphical method is not exact.
Key Terms
simultaneous equations, substitution method,
graphical method |
