24
T
T
H
H
E
E
L
L
I
I
N
N
E
E
A
A
R
R
S
S
O
O
L
L
V
V
E
E
R
R
A
A
P
P
L
L
E
E
T
T
This is a very easy aplet to use. It is designed to solve simultaneous
linear equations in 2 or 3 unknowns. If there is a solution it will display
it. Otherwise it will indicate whether there is no solution or an infinite
number of solutions.
E
E
x
x
a
a
m
m
p
p
l
l
e
e
1
1
Solve the system of equations:
2
x
y
z
3
+
− =
2.5
⎫
⎪
+ =
1.5
⎬
x
z
−
2
⎭
3
y
z
=
1.5
⎪
In the Aplet view,
the aplet and you will see the view shown
right.
Enter the coefficients from the equations, including zeros for any missing
coefficients. Negative coefficients must be entered using the
button
rather than using ‘subtract’.
As you do so the solution will be displayed at the bottom of the screen.
In this case there is a unique solution of
x = -1
,
y = 2.5
and
z = 3
.
E
E
x
x
a
a
m
m
p
p
l
l
e
e
2
2
Solve the system of equations:
+
3
2
x
y
=
5
⎫
⎬
+
3
2
x
y
=
7
⎭
As you may be able to see, this is a pair of parallel lines and so has no
solution. To see this on the calculator we must first change to the 2x2
view, meaning 2 equations in 2 unknowns. At the bottom of the screen
you will see buttons labeled
and
. Currently the 3x3
button should be selected, as shown by the dot next to it on the label:
. Click on the
button and it will change into the 2x2 view
as shown above right.
Enter the coefficients for the equations above. As you can see in the
screenshot to the right, the result is shown as “No solutions” as expected.
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