Using a TI-84 calculator, hit 2nd x^-1 or the "matrix" function.
Arrow right 2 spots to the "edit" tab and hit enter.
Type in 3 x 4. 3 enter. 4 enter.
Your matrix to solve is a 3 x 4 matrix as the problem above indicates.
(Rows by Columns, thus 3 rows and 4 columns is a 3 x 4 matrix).
Now enter the leading coefficient of each row into the calculator until all 12 values are entered into your calculator matrix.
i.e. - row 1 = 2 enter, 3 enter, -1 enter, 6 enter.
row 2 = 3 enter, 1 enter, 5 enter, 8 enter.
row 3 = 1 enter, 2 enter, 1 enter, 10 enter.
Now, hit 2nd mode(quit) button on calculator.
Then, hit matrix button again.
Arrow over 1 to the right to "math". Alist will appear. Arrow down until you see "rref" - which is letter B on my calculator.
Hit 2nd Matrix key again. Hit enter (on matrix A).
Close the parentheses on calculator by hitting right parentheses ")".
This shows your solution to your matrix.
The 3 values in the far right column are your values to x, y, and z.
The answer should probably be stated in fraction form, not decimal forms that have appeared.
To covert to fractions, hit "MATH" button on calculator, hit enter, hit enter again, and now your matrix has been converted to fractions.
The answers I get are:
x = -66/17.
y = 94/17.
z = 48/17.
(Answers in decimal form are:)
x = -3.882352941.
y = 5.529411765.
z = 2.823529412.
You can check your answers by substituting these answers into any or all of the 3 equations given in your problem and making sure that the result is a true statement.