Question 33798
2x-5y+ ___=-22...........................I
__+y+3z=10.....................II
x+___+8z=15...........................III

2*EQN.III-EQN.I
2X+16Z-2X+5Y=30+22=52
5Y+16Z=52...........................IV
EQN.IV-5*EQN.II
5Y+16Z-5Y-15Z=52-50=2
Z=2....SUBSTITUTING IN EQN.III
X+8*2=15
X=15-16=-1
SUBSTITUTING FOR Z IN EQN.II
Y+3*2=10
Y=10-6=4

USING MATRIX METHOD...AUGMENTED MATRIX IS 

2	-5	0	-22		1	0	0	?
0	1	3	10		0	1	0	?
1	0	8	15		0	0	1	?

NR1=R1/2								

1	-2.5	0	-11					
0	1	3	10					
1	0	8	15					
								
NR3=R3-R1								
			
1	-2.5	0	-11
0	1	3	10
0	2.5	8	26
			
NR3=R3-2.5*R2			
			
1	-2.5	0	-11
0	1	3	10
0	0	0.5	1
			
NR3=R3/0.5			
			
1	-2.5	0	-11
0	1	3	10
0	0	1	2
			
NR2=R2-3R3			
			
1	-2.5	0	-11
0	1	0	4
0	0	1	2

NR1=R1+2.5R2			
			
1	0	0	-1
0	1	0	4
0	0	1	2
			
HENCE 			
X=-1			
Y=4			
Z=2