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There are many situations in which scientists, mathematicians, engineers
and others have to consider problems involving more than one variable.
Consider the following two equations which contain the unknowns x
and y.
If we determine the values of x and y such that equations
(1) and (2) hold true, then the two equations are called simultaneous
equations as they are considered together.
Simultaneous equations are solved approximately using the graphical
method or exactly using an algebraic method.
The Graphical Method
The graphical solution of linear simultaneous equations is the
point of intersection found by drawing the two linear equations on the
same axes.
Example 1
Solve the following simultaneous equations graphically.
Solution:
The graphical solution of the simultaneous equations
is given by the point of intersection of the linear equations.
Consider x + y = 8.
x-intercept:
When y = 0, x = 8
y-intercept:
When x = 0, y = 8
Consider x – y = 2.
x-intercept:
When y = 0, x = 2
y-intercept:
The diagram shows that the lines intersect at the point (5, 3). So, the
solution of the simultaneous equations is x = 5 and y = 3 or
(5, 3).
Note:
Often the answer obtained with the graphical method is not exact.
Key Terms
simultaneous
equations, graphical method
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