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31 October, 23:09

Solve the following 3 * 3 system. Enter the coordinates of the solution below.

2x - 3y - 2z = 4

x + 3y + 2z = - 7

-4x - 4y - 2z = 10

+1
Answers (1)
  1. 1 November, 02:37
    +1
    The system of equations is

    2x - 3y - 2z = 4 (1)

    x + 3y + 2z = - 7 (2)

    -4x - 4y - 2z = 10 (3)

    There are many methods for solving the system of equations, including matrix methods. I shall use basic algebraic methods.

    Subtract (3) from (1).

    6x + y = - 6 (4)

    Add (2) and (3).

    -3x - y = 3 (5)

    Add (4) and (5).

    3x = - 3

    x = - 1

    From (4), obtain

    y = - 6 - 6x

    = - 6 + 6

    = 0

    From (2), obtain

    2z = - 7 - x - 3y

    = - 7 + 1

    = - 6

    z = - 3

    Answer: (-1, 0, - 3)

    The solution is x = - 1, y = 0, z = - 3.
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