Question 54320
2x-y+4z=-2 (E1)
3x-2y-z=-3  (E2)
x+4y+2z=17  (E3)
: Eliminate z in (E1) and (E2) by multiplying 4*(E2) and adding the two equations.
2x-y+4z=-2----------> 2x- y+4z=-2
4(3x-2y-z)=4(-3)---->12x-8y-4z=-12
:
 2x- y+4z=-2
12x-8y-4z=-12
_____________
14x-9y+0z=-14
14x-9y=-14 (E4)
:Eliminate the z using 2*(E2) + (E3). 
2(3x-2y-z)=2(-3)------->6x-4y-2z=-6
x+4y+2z=17-------------> x+4y+2z=17
:
6x-4y-2z=-6
+x+4y+2z=17
_____________
7x+0y+0z=11
7x=11
7x/7=11/7
x=11/7
:Substitute x=11/7 into (E4) and solve for y:
14(11/7)-9y=-14
{{{154/7-9y=-14}}}  Clear the fraction by multiplying everything by 7 to make it easier to solve.
{{{7*154/7+7(-9y)=7(-14)}}}
{{{cross(7)154/cross(7)-63y=-98}}}
154-63y=-98
-154+154-63y=-98-154
-63y=-252
-63y/-63=-252/-63
y=4
:
Substitute x=11/7 and y=4 into (E2).
3(11/4)-2(4)-z=-3
Work that out and you get z=-2/7
So your answer is (11/7,4,-2/7)
Don't forget to check your answer by sustituting these values into all three original equations.
Let me know if you need more explanation.
Happy Calculating!!!