Question 916125
x+(1/3y)+z=13
(1/2x)-y+(1/3z)=-2
x+(1/2y)-(1/3z)=2

Take LCM and simplify the equations to eliminate the denominators

3      	x	+	1      	y	+	3      	z	=	39      			--------------				1
3      	x	+	-6      	y		2      	z	=	-12      			--------------				2
6      	x	+	3      	y	+	-2      	z	=	12      			--------------				3
																
consider equation 1 &2				Eliminate	y											
Multiply 1 by		6      					-5      									
Multiply 2 by		1      					4      									
we get																
18      	x		+	6      	y	+	18      	z	=	234						
3      	x		+	-6      	y	+	2      	z	=	-12						
Add the two																
21      	x		+	0      	y	+	20      	z	=	222	-------------				4	
consider equation 2 & 3				Eliminate	y											
Multiply 2 by				1      												
Multiply 3 by				2      												
we get																
3      	x	+	-6      	y	+	2      	z	=	-12      							
12      	x	+	6      	y	+	-4      	z	=	24      							
Add the two																
15      	x	+	0      	y	+	-2      	z	=	12      	-------------5				5		
Consider (4) & (5)			Eliminate	x												
Multiply 4 by				-15      												
Multiply (5) by				21      												
we get																
-315      	x	+	-300      	z	=	-3330      										
315      	x	+	-42      	z	=	252      										
Add the two																
0      	x	+	-342      	z	=	-3078      										
/	-342      															
z	=	9      														
15      	x	+	-2      	z=	12      											
15      	x	+	-18      	=	12      											
			x	=	2      											
Plug x & z in eq (1)																
3      	x	+	1      	y	+	3      	z	=	39      			--------------				1
	6      	+	1      	y	+	27      		=	39      							
			1      	y				=	6      							
				y	=				6      							
	x=	2      	y=	6      	z=	9