A TI83 will be useful here. Method
1: Graphing
 We start by presing [ Y = ] (top right).
This will bring up a screen in which we will enter equation (1)
into Y1 and equation (2) into Y2.
 Make sure you set the [ WINDOW ] (top
second right) in a way that you will be able to see the intersection,
if there is one.
 Press [ GRAPH ] (top left). This will
plot your graphs.
 Press [ 2nd ] [
TRACE ] to obtain the CALC
function that brings us to a page called "CALCULATE". Scroll down
to " 5:intersect " and press [ ENTER ] .
 The first prompt is "First curve?" and there will be a blinker
on the first curve Y1. The equation Y1 is displayed on the upper
left. Make sure that this is correct. If it is correct then press
[ ENTER ] . It will then ask for the "Second
curve?" and again make sure that it is Y2. If it is correct then
press [ ENTER ] . The last prompt is "Guess?".
Moves your blinker to the intersection and press
[ ENTER ]. The intersection point is reported at the bottom
of the screen.
Method 2: Matrix Method
For illustration, we going to use a previous example of
 5x + 2y = 10 ; (1)
4x  3y = 12 ; (2)
For this technique to work, always arrange your equations
with x first and then y as we had done here. [You could have y first
and then x but not one equation with x first and the second equation
with y first.]
Press
[2nd][x^{1}] for Matrix and move to EDIT as in Screen 1.
The dimension of the matrix is 2x3 ("2 by 3") where 2 stands
for 2 equations and 3 terms in our case. The number 10 in equation
1 is taken as a term. Enter the information as in Screen 2.
Press[2nd][MODE] to quit from the matrix entry. Press [2nd][x^{1}]
for Matrix again and move to Math and B:rref as in Screen 3. Press
[ENTER] [2nd][x^{1}] and at Names select 1:[A] and [ENTER].
We will now obtain the top three lines in Screen 4. It is a good practice
to change the answers back to fraction. Thus, press [MATH] , select
1:>Frac [ENTER] to obtain the results in Screen 4.
We will report the answer as x = 54/7 and y = 100/7.
The rref stands for reduced rowechelon
form but for our purpose this is a symbol that helps
us to solve simultaneous equations. This method can also be used for
3 equations with 3 variables. In general, this method works for n
equations with n variables.
Method 3: Use the Application
Polysmlt from Ti. This application is acceptable for IB examination
and can be downloaded from here.
