Question 114043: Solve this system of equations.
x+y+z= -1
2x+4y+2z= -2
-x+6y-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 josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! x + y + z = -1
2x + 4y + 2z = -2
-x + 6y - 3z = -21
divide 2nd one by 2
x + 2y + z = -1
multiply each side by -1
-x - 2y - z = 1
add it to the 1st one
x + y + z = -1
-x - 2y - z = 1
y - 2y = 0
-y = 0
multiply both sides by -1
y = 0
The 3rd equation is
-x + 6y - 3z = -21
y = 0
-x - 3z = -21
The 1st equation is
x + y + z = -1
y = 0
x + z = -1
add the 3rd and 1st
-2z = -22
z = 11
The 2nd one is
-x - 2y - z = 1
y = 0
z = 11
-x - 11 = 1
-x = 12
x = -12
The solutions are x = -12, y = 0, z = 11
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