SOLUTION: I need help solving this system. Thank you.
2x - y - z = 1
x + 2y + z = 0
3x - y - 2z = -1
Algebra.Com
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
RELATED QUESTIONS
I need help solving each system. Thank you.
2x-y-z=1
x+2y+z=0... (answered by josgarithmetic,richwmiller)
I need help solving each system. Thank you.
x-2y-z=3
2x+y-2z=1... (answered by lwsshak3)
Need help solving system with three variables
x + y + z = 0
2x+ 3y + 2z = -3
-x - 2y (answered by ikleyn)
How do you solve this three-variable system?
{x+2y+z=4
{2x-y+4z=-8... (answered by Alan3354)
Solve the System:
2x-y+2z=11
3x-2y-z=12... (answered by Electrified_Levi)
Solving systemn of equations in three variables
x-y-Z=0
2x-3y+2z=7
-x+2y+z=1... (answered by ikleyn)
OK, I think that I got this right but I would like a double check please.
Set up an... (answered by richwmiller)
Use the elimination method to solve the following system of equations. what is z,y & z... (answered by TimothyLamb)
3x-y+z=5
X+-2y-z=1... (answered by Fombitz)