Question 888524: I need help solving this system. Thank you.
2x - y - z = 1
x + 2y + z = 0
3x - y - 2z = -1
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 2x - y - z = 1
x + 2y + z = 0
3x - y - 2z = -1
2,-1,-1,1
1,2,1,0
3,-1,-2,-1
divide row 1 by 2/1
1,-1/2,-1/2,1/2
1,2,1,0
3,-1,-2,-1
add down (-1/1) *row 1 to row 2
1,-1/2,-1/2,1/2
0,5/2,3/2,-1/2
3,-1,-2,-1
add down (-3/1) *row 1 to row 3
1,-1/2,-1/2,1/2
0,5/2,3/2,-1/2
0,1/2,-1/2,-5/2
divide row 2 by 5/2
1,-1/2,-1/2,1/2
0,1,6/10,-2/10
0,1/2,-1/2,-5/2
add down (-1/2) *row 2 to row 3
1,-1/2,-1/2,1/2
0,1,3/5,-1/5
0,0,-16/20,-48/20
divide row 3 by -4/5
1,-1/2,-1/2,1/2
0,1,3/5,-1/5
0,0,1,3
z=3
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-3/5) *row 3 to row 2
1,-1/2,-1/2,1/2
0,1,0,-2
0,0,1,3
y=-2
add up (1/2) *row 3 to row 1
1,-2/4,0,2
0,1,0,-2
0,0,1,3
add up (1/2) *row 2 to row 1
1,0,0,1
0,1,0,-2
0,0,1,3
x=1
final
1,0,0,1
0,1,0,-2
0,0,1,3
x=1
y=-2
z=3
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