How do i solve this system of equations?
3x-y+z=-1
3x+2y-5z=-16
3x+3y+2z=6

  (x, y, z) = (-1, 1, 3)

Step-by-step explanation:

You can solve this system by any of the methods you have been taught. These methods probably include elimination, substitution, and perhaps matrix methods. Spreadsheets and graphing calculators can also help you solve these.

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Since the x-coefficients are the same on all of these equations, it is easy to eliminate the x-terms by subtracting one equation from another.

Subtracting the first from the second gives ...

  (3x +2y -5z) -(3x -y +z) = (-16) -(-1)

  3y -6z = -15 . . . . . simplify

  y -2z = -5 . . . . . . . divide by 3 [eq4]

Subtracting the first from the third gives ...

  (3x +3y +2z) -(3x -y +z) = (6) -(-1)

  4y +z = 7 . . . . . . . simplify [eq5]

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Now, we can add [eq4] to twice [eq5] to eliminate z:

  2(4y +z) +(y -2z) = 2(7) +(-5)

  9y = 9 . . . . . simplify

  y = 1 . . . . . . . divide by 9

Using [eq5], we can find z:

  4(1) +z = 7

  z = 3 . . . . . . subtract 4

Using the first equation, we can find x.

  3x -(1) +(3) = -1

  3x = -3 . . . . subtract 2

  x = -1 . . . . . . divide by 3

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step-by-step explanation:

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