Question 298763
<pre>
{{{system(-10x+14y+3z=74,
x+17y+9z = 85,
-13x-8y+3z=14)}}}
----------------------------------
{{{system(red(-10)x+red(14)y+red(3)z=red(74),
red(1)x+red(17)y+red(9)z = red(85),
red(-13)x+red(-8)y+red(3)z=red(14))}}}
<pre><font size = 4 color = "indigo"><b>
Put all those red numbers in a 3x4 augmented matrix
like this:

{{{red((matrix(3,5,

-10,14,3,"|",74,
  1,17,9,"|",85,
-13,-8,3,"|",14)))}}}

On your TI-83 or TI-84,

Press CLEAR

Press 2ND
Press x<sup>-1</sup> (MATRIX)
Prees the right arrow twice to highlight EDIT
Press ENTER
Press 3
Press ENTER
Press 4
Press ENTER
Type -10, 
Press ENTER
Type 14,
Press ENTER
Type 3,
Press ENTER
Type 74
Press ENTER
Type 1
Press ENTER
...
continue typing in all the rest of the elements 
in the matrix, pressing ENTER after each. Then
...
Press 2ND
Press MODE (QUIT)
Press 2ND
Press x<sup>-1</sup> (MATRIX)
Press right arrow to highlight MATH
Press up arrow 5 times to highlight B:rref(
Press ENTER  you should see rref( on the screen
Press 2nd
Press x<sup>-1</sup> (MATRIX)
Press ENTER  you should see rref([A]
Press ENTER

You should see  

rref([A]
    [[1 0 0 -2]
     [0 1 0 3 ]
     [0 0 1 4 ]]

Interpret this as the system:

{{{system(1x+0y+0z=-2,0x+1y+1z=3, 0x+0y+1z=4)}}}

or

{{{system(x=-2,y=3,z=4)}}}  
Edwin</pre>