The first example we used was:
4
0
3
7
x
y
x
y

=
+
=
In order to be able to solve this system we have to rewrite the system in a
way that
y
is expressed in terms of
x
in both equations, as follows:
4
0
4
3
7
7
3
x
y
y
x
x
y
y
x

=
⇒
=
+
=
⇒
=

Now what we have to do is to plot these two graphs and their intersection
should give us the solution to our problem.
10
8
6
4
2
0
2
4
6
8
10
4
2
0
2
4
6
8
10
12
14
4
y
x
=
7
3
y
x
=

(1,4)
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35
According to the plot of the two graphs the solution to our problem is
1
4
x
and y
=
=
, which is exactly what we got earlier. However, we must admit
we have cheated a little bit by plotting the graphs using a mathematical
software. However, imagine we have to plot these graphs by hand it will not
be easy to get the exact solution, even with graphical papers sometimes. This
is one drawback of using the graphical method to solve simultaneous
equations.
We can also try to solve our second problem by graphical method.
6
2
3
1
2
4
6
4
6
2
4
4
2
2
3
4
4
4
3
3
3
3
4
1
3
3
3
x
y
y
x
x
y
y
x
x
x
y
y
x
y
y
x
=

⇒
=

+
=
⇒
=

⇒


=
⇒ 
=
+
⇒
=
+
⇒
=  

