Write each equation in terms of Y. For example, for 15x - 3y = 6:
15x - 3y = 6
-3y = -15x + 6
3y = 15x - 6
y = 5x - 2
Turn on your TI-83.
Press the "Y=" button.
Enter each equation into a separate function. All you need to enter is the information on the side of the equation opposite Y.
Go to the CALC menu. The CALC menu can be accessed by hitting the "2nd" key and then the TRACE button.
Select "Intersect" from the CALC menu.
Select the two functions you wish to calculate the intersect of, and then enter a guess. You may skip the guessing part by simply pressing enter. The TI-83 will return a value of X and Y. This is the solution point to your system of equations.
Access the Matrix menu by pressing the MATRX key. On a TI-83 Plus, the Matrix menu is accessible by pressing "2nd" and then the "x^-1" key.
Modify matrix [A] so that is an A by B matrix, where A is the number of equations in your system and B is the number of terms in each equation, including constants. For example, for the following system of equations:
3x + 5y = 43
2y - 3x = -8
x - y = 1
Matrix [A] will be 3 by 3.
Write your system of equations such that all similar variables are aligned in columns. For example:
3x + 5y = 43
2y - 3x = -8
x - y = 1
becomes
3x + 5y = 43
-3x + 2y = -8
x - y = 1
Enter the coefficients and constants into matrix [A]. For example:
[ 3 5 43
-3 2 -8
1 -1 1 ]
Exit the edit screen by hitting the "2nd" button and then the MODE button.
Go to the matrix MATH sub-menu by hitting the MATRX key again.
Select the "rref(" item on the MATH list.
Specify matrix [A] as the parameter for the rref function.
Hit ENTER. The solution matrix will display. You can read the corresponding matrix by looking at the last column. The last column shows the value of the variable corresponding to the 1 in the row alongside it. The 1 corresponds to the position of that variable in the original matrix. For example:
[ 1 0 6
0 1 5
0 0 0 ]
The 6 corresponds to the x-value, the 5 corresponds to the y-value.