4x-4y+4z=8 9x+3y+z=6 16x+4y+z=2

Question

4x-4y+4z=8
9x+3y+z=6
16x+4y+z=2

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Thạch Thảo 3 years 2021-08-02T02:05:14+00:00 1 Answers 3 views 0

Answers ( )

  1. kiet
    0
    2021-08-02T02:06:22+00:00
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    9514 1404 393

    Answer:

      (x, y, z) = (-1, 3, 6)

    Step-by-step explanation:

    The augmented matrix for the system is …

      \left[\begin{array}{ccc|c}4&-4&4&8\\9&3&1&6\\16&4&1&2\end{array}\right]

    Your graphing or scientific calculator can tell you the solution to this system is …

      (x, y, z) = (-1, 3, 6)

    __

    If you want to solve this by hand, it can work well to divide the first equation by 4 to get …

      x -y +z = 2

    This can be subtracted from the other two equations to eliminate z.

      (9x +3y +z) -(x -y +z) = (6) -(2)  ⇒  8x +4y = 4

      (16x +4y +z) -(x -y +z) = (2) -(2)  ⇒  15x +5y = 0

    These two equations can be reduced to standard form:

    • 2x +y = 1
    • 3x +y = 0

    Subtracting the first equation from the second, we have …

      (3x +y) -(2x +y) = (0) -(1)  ⇒  x = -1

    Substituting into the first gives y:

      2(-1) +y = 1

      y = 3 . . . . . . . add 2

    Then we can find z from the reduced first equation above:

      z = 2 -x +y = 2 -(-1) +3 = 6

    Then the solution is (x, y, z) = (-1, 3, 6).

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )