Question 1101719
<pre>

2v +  w + 2x - 2y +  z = 10
 v + 2w + 3x + 3y - 3z = -6
 v -  w - 2x - 2y + 3z =  8
2v - 2w +  x - 3y + 2z = 15
3v + 3w -  x +  y -  z =  1

It's too much to ask of any student to solve this
by hand and without technology.  So I'll do it using
a TI-84.  If your teacher doesn't allow this, then he
or she is unreasonable and should be fired.

Make the augmented matrix

{{{(matrix(5,7,

2,  1,  2, -2,  1, "|", 10,
1,  2,  3,  3, -3, "|", -6,
1, -1, -2, -2,  3, "|",  8,
2, -2,  1, -3,  2, "|", 15,
3,  3, -1,  1, -1, "|",  1 ))}}}

Put that in your TI-84 by pressing 2ND x<sup>-1</sup>

Highlight EDIT
Make it read 5 x6 and enter the 30 matrix numbers left to
right, top to bottom

Press 2ND MODE
Press CLEAR
Press 2ND x<sup>-1</sup>
Highlight MATH
Scroll to highlight B:rref(
Press ENTER

   Screen will read rref(
Press 2ND x<sup>-1</sup>
Press ENTER
Press ) to close the parentheses
   Screen will read rref([A])
Press MATH ENTER ENTER

Screen reads

{{{matrix(5,6,

1,  0,  0,  0,  0, 178/75,
0,  1,  0,  0,  0, -71/75,
0,  0,  1,  0,  0, 14/25,
0,  0,  0,  1,  0, -59/25,
0,  0,  0,  0,  1,  9/25 )}}}

which means

v = 178/75
w = -71/75
x =  14/25
y = -59/25
z =   9/25 

I'll say again, if your teacher said to do that by hand and
not use a calculator or technology, then he or she is totally
unreasonable and should be fired.

Edwin</pre>