Question 258522
Lets take this  one step at a time. Here is the original problem:
(i) 4x+2y+z=7
(ii) 2x+2y-4z=-4
(iii) x+3y-2z=-8 
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basically, we want to kill a variable. getting rid of X look pretty easy
step 1 -> ROW 1 - 2 x ROW 2 AND ROW 2 - 2 x ROW 3 to get
(iv) -2y + 9z = 15
(v) -4y = 12
Luck y us, we can get y right away as
{{{y = -3}}}
step 2 -> put the value of y back into (iv) to get y as
-2(-3) + 9z = 15
9z = 9
{{{z=1}}}
Put the values of z and y into (i) to get x as
4x + 2(-3) + (1) = 7
4x -6 + 1 = 7
4x - 5 = 7
4x = 12
{{{x = 3}}}
so (x,y,z) = (3, -3, 1)