Solution using Gauss-Jordan reduction: As in the first solution (elimination method), we first make sure the two equations are “lined up” properly.
2x + 3y = 7
3x + 5y = 5
We’ll use our TI-84 Calculator now. Begin by pushing the MATRIX button. Scroll over to EDIT and then select A. We will be inputting a 2×3 matrix, so press 2 ENTER 3 ENTER. We then begin entering the numbers 2, 3, and 7 for the first row, and 3, 5, and 5 for the second row. To do this we can simply type 2 ENTER 3 ENTER 7 ENTER 3 ENTER 5 ENTER 5 ENTER.
Note: What we have just done was create the augmented matrix for the system of equations. This is simply an array of numbers which contains the coefficients of the variables together with the right hand sides of the equations.
Now push the QUIT button (2ND MODE) to get a blank screen. Press MATRIX again. This time scroll over to MATH and select rref( (or press B). Then press MATRIX again and select A and press ENTER.
Note: What we have just done is put the matrix into reduced row echelon form. In this form we can read off the solution to the original system of equations.
Warning: Be careful to use the rref( button (2 r’s), and not the ref( button (which has only one r).
The display will show the following.
[ [1 0 20]
[0 1-11]]
The first line is interpreted as x = 20 and the second line as y = -11.
So we have
(y + 1)/x = (-11 + 1)/20 = -10/20 = -1/2, choice (B).