SOLUTION: Solve this system of equations. x+ y+ z= 1 2x+y+2z= -2 -x+y-3z= -21 Write the solution as an ordered triple. ( ) (Type an exact answer in simplified fo

Question 114016: Solve this system of equations.
x+ y+ z= 1
2x+y+2z= -2
-x+y-3z= -21

Write the solution as an ordered triple.
( )
(Type an exact answer in simplified form. If the solution is the empty set, type N for each coordinate. If there are infinitely many solutions, type I for each coordinate.)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
x + y + z = 1
2x+ y +2z = -2
-x+ y -3z = -21
:
x + y + z = 1
2x+ y +2z = -2
-x+ y -3z = -21
------------------Adding eliminates z
2x + 3y = -22
:
Multiply the 1st equation by 3 and add to it equation 3
3x + 3y + 3z = 3
-x + y - 3z = -21
-------------------adding eliminates z again
2x + 4y = -18
:
Using these two, 2 unknown equations, subtract the 1st one from the 2nd one:
2x + 4y = -18
2x + 3y = -22
------------------subtracting eliminates x
0x + y = + 4
y = +4
:
Find x using 2x + 4y = -18
2x + 4(4) = -18
2x + 16 = -18
2x = -18 - 16
2x = -34
x = -17
:
I'll let you find z. Check solutions in one of original equations
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