Question 1060073
.
Solve the system of equations. 
(If the system is dependent, enter a general solution in terms of c. 
If there is no solution, enter NO SOLUTION.)

2x	 − 	y	 + 	z	 = 	12
2y	 − 	3z	 = 	−16
3y	 + 	2z	 = 	2
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2x -  y +  z =  12,    (1)
     2y - 3z = -16,    (2)
     3y + 2z =   2.    (3)

Notice that the equations (2) and (3) constitute a closed 2x2-sub-system.
   (I use the term "closed sub-system" to highlight that these two equations are for two unknowns y and z and do not include "x".)

For it, multiply eq.(2) by 2 and eq(3) by 3, then add. You will get

4y + 9y + (-6z + 6z) = -32 + 6,   or

13y = -26  --->  y = -2.

Then from (3)  2z = 2 - 3y = 2 - 3*(-2) = 2 + 6 = 8  --->  z = 4.

Next, substitute the found values y and z into equation (1) and get x = 3.


<U>Answer</U>.  x= 3, y= -2, z= 4.
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