Solve the following system of equations for all three variables. -7x+y+z= −7x+y+z= \,\,-9 −9 -7x+5y-9z=

Question

Solve the following system of equations for all three variables.
-7x+y+z=
−7x+y+z=
\,\,-9
−9
-7x+5y-9z=
−7x+5y−9z=
\,\,-3
−3
7x-6y+4z=
7x−6y+4z=
\,\,-6
−6

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Sarah 3 weeks 2021-09-24T20:44:49+00:00 1 Answer 0

Answers ( )

    0
    2021-09-24T20:46:16+00:00

    Answer:

    (x,y,z) -> (2,4,1)

    Step-by-step explanation:

    -7x + y + z = -9

    -7x + 5y – 9z = -3

    7x – 6y + 4z = -6

    Pick two pairs:

    -7x + 5y – 9z = -3

    7x – 6y + 4z = -6

    and

    -7x + y + z = -9

    -7x + 5y – 9z = -3

    Eliminate the same variable from each system:

    -7x + 5y – 9z = -3

    7x – 6y + 4z = -6

    + 5y – 9z = -3

    – 6y + 4z = -6

    -1y – 5z = – 9

    -7x + y + z = -9

    -7x + 5y – 9z = -3

    -7x + y + z = -9

    7x – 5y + 9z = 3

    -4y – 10z = -6

    Solve the system of the two new equations:

    -1y – 5z = – 9           ->      -4 ( -1y – 5z = – 9)     ->   4y + 20z = 36  

    -4y – 10z = -6          ->           -4y – 10z = -6      ->   -4y – 10z = -6

    10z = 30

    Thus, z = 3

    -4y – 10z = -6

    -4y – 10(3) = -6

    -4y – 30 = -6

    -4y = 24

    Thus, y = -6

    Substitute into one of the original equations:

    -7x + y + z = -9

    -7x + (-6) + (3) = -9

    7x + -3  = -9

    7x  = -6

    x =

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