Solve the system 6x -2y+z= -2 2x+ 3y – 3z =11 x+ 6y=31

Question

Solve the system 6x -2y+z= -2 2x+ 3y – 3z =11 x+ 6y=31

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niczorrrr 5 years 2021-08-13T13:58:07+00:00 1 Answers 19 views 0

Answers ( )

  1. Sigrid
    0
    2021-08-13T13:59:56+00:00
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    Answer:

    x = 1

    y = 5

    z = 2

    Step-by-step explanation:

    System of equations:

    6x – 2y + z = -2

    2x + 3y – 3z = 11

    x + 6y = 31

    Isolate one variable in any of the equations:

    x + 6y = 31

    x = 31 – 6y

    Plug in this value for x in another equation:

    6(31 – 6y) – 2y + z = -2

    186 – 36y – 2y + z = -2

    186 – 38y + z = -2

    -38y + z = -188

    z = -188 + 38y

    Plug in these values in the remaining equation:

    2(31 – 6y) + 3y – 3(-188 + 38y) = 11

    62 – 12y + 3y + 564 – 114y = 11

    626 – 12y + 3y – 114y = 11

    626 – 9y – 114y = 11

    626 – 123y = 11

    -123y = -615

    y = 5

    Plug in value of y into our other answers to solve for x and z:

    x = 31 – 6(5)

    x = 31 – 30

    x = 1

    z = -188 + 38(5)

    z = -188 + 190

    z = 2

    Check your work:

    6x – 2y + z = -2

    6(1) – 2(5) + 2 = -2

    6 – 10 + 2 = -2

    -4 + 2 = -2

    -2 = -2

    Correct!

    *Note there are several ways to solve for these types of problems. I used substitution*

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