Question 1175220
Find the solution to the system of equations:

(x - 2y + z = -3
|y + 2z = -5
|x + y + 3z = -6
<pre>This is NOT as COMPLEX as the other "respondents" make it seem! {{{matrix(3,3, x - 2y + z, "=", - 3, y + 2z, "=", - 5, x + y + 3z, "=", - 6)}}}
EASISET/QUICKEST/LEAST TIME-CONSUMING method, as follows: 

 x - 2y +  z = - 3 ------ eq (i)
      y + 2z = - 5 ------ eq (ii)
 x +  y + 3z = - 6 ------ eq (iii)
     3y + 2z = - 3 ------ Subtracting eq (i) from eq (iii) ------ eq (iv)
2y = 2 ------- Subtracting eq (ii) from eq (iv)
{{{highlight_green(matrix(1,5, highlight(y), "=", 2/2, "=", highlight(1)))}}}

1 + 2z = - 5 ------- Substituting 1 for y in eq (ii)
2z = - 5 - 1
2z = - 6
{{{highlight_green(matrix(1,5,  highlight(z), "=", (- 6)/2, "=",  highlight(- 3)))}}}

x - 2(1) + - 3 = - 3 ------- Substituting 1 for y in eq (ii)
x - 2 - 3 = - 3
x - 5 = - 3
{{{highlight_green(matrix(1,5,  highlight(x), "=", - 3 + 5, "=",  highlight(2)))}}}</pre>