Solving Simultaneous Equations - HP 39gs Master Manual

S o l v i n g s i m u l t a
S o l v i n g s i m u l t a
Solve the systems of equations below:
(i)
Method 1 - Graphing the lines
Because the first set of equations is a 2x2 system it can be graphed in
the Function aplet. To do this it is necessary to re-arrange the functions
into the form y = ...... and store them into
view of the Function aplet. Switch to the
SYMB
tool to find the point of intersection.
Intersection
It is worth noting that although the point of intersection is on the screen
here, this is not necessary. The
if neither line is visible on the currently set axes.
Method 2 - Using a matrix
Step 1. Rewrite
This means that
Step 2. Switch into the Matrix Catalog (
the highlight on
right.
Press
SHIFT MATRIX
create as shown below right. Note that setting
M2
make it easier to enter
n e o u s e q u a t i o n
n e o u s e q u a t i o n
− 3 y = − 7 ⎫
2 x
⎬
+ 4 y = 2 ⎭
x
F1(X)
Intersection
− 3 y = −7 ⎫
2x
as
⎬
+ 4 y = 2 ⎭
x
− 1
⎡ 2 −3 ⎤ ⎡ −7 ⎤
x ⎡ ⎤
⎢ ⎥ = ⎢ × ⎢
4 ⎦ ⎥
y ⎣ ⎦ ⎣ 1 ⎣ 2 ⎦
SHIFT MATRIX
and press . Enter the matrix shown
M1
to change back to the catalog view and
.
M2
s .
s .
2x y = 4 −
− + 2 − = −10.5
(ii)
3x y z
− 3 + y z = 10.5
x
and in the
F2(X)
view and use the
PLOT
tool will work even
⎡ 2 −3 ⎤ ⎡ ⎤ ⎡ −7 ⎤
x
=
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ 1 4 ⎦ ⎣ ⎦ ⎣ 2 ⎦
y
⎥
). Position
will
302