SOLUTION: This is a systems of equations problem and I need to solve for x,y,z. I do not how to get any of the variables or what steps to take to get the answers. The problem: 2x-5y+ __

SOLUTION: This is a systems of equations problem and I need to solve for x,y,z. I do not how to get any of the variables or what steps to take to get the answers. The problem: 2x-5y+ ___=

Question 33798: This is a systems of equations problem and I need to solve for x,y,z. I do not how to get any of the variables or what steps to take to get the answers.
The problem:
2x-5y+ ___=-22
__+y+3z=10
x+___+8z=15
The underscores represents blanks or O
If this had to be an augmented matrix, how would I do that and get those variables?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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
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