Question 907208: 5x-y+z=4, 3x=2y-3z=36, x-3y+2z=-25 Complete the ordered triple
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Assuming that is +2y in the second equation
(3,6,-5)
5,-1,1,4
3,2,-3,36
1,-3,2,-25
divide row 1 by 5
1,-1/5,1/5,4/5
3,2,-3,36
1,-3,2,-25
add down (-3) *row 1 to row 2
1,-1/5,1/5,4/5
0,13/5,-18/5,168/5
1,-3,2,-25
add down (-1) *row 1 to row 3
1,-1/5,1/5,4/5
0,13/5,-18/5,168/5
0,-14/5,9/5,-129/5
divide row 2 by 13/5
1,-1/5,1/5,4/5
0,1,-90/65,840/65
0,-14/5,9/5,-129/5
add down (14/5) *row 2 to row 3
1,-1/5,1/5,4/5
0,1,-18/13,168/13
0,0,-675/325,3375/325
divide row 3 by -27/13
1,-1/5,1/5,4/5
0,1,-18/13,168/13
0,0,1,-5
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (18/13) *row 3 to row 2
1,-1/5,1/5,4/5
0,1,0,6
0,0,1,-5
add up (-1/5) *row 3 to row 1
1,-5/25,0,45/25
0,1,0,6
0,0,1,-5
add up (5/25) *row 2 to row 1
1,0,0,3
0,1,0,6
0,0,1,-5
final
1,0,0,3
0,1,0,6
0,0,1,-5
1,0,0,3
0,1,0,6
0,0,1,-5
"3","6","-5"
(3,6,-5)
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