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Solve each system of equations. Let z be the parameter.?

x + 2y + 3z = 11

2x – y + z = 2

Please explain in detail if you can I am trying to learn how to do these. Thanks...

2 Answers

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  • 1 decade ago
    Favorite Answer

    1)

    x + 2y + 3z = 11 …(a1)

    -------------------------x2

    2x + 4y + 6z = 22 …(a2)

    A1 and A2 are the same equation

    2)

    2x – y + z = 2 …(b1)

    -------------------------x2

    4x – 2y + 2z = 4 …(b2)

    B1 and B2 are the same equation

    3) A1 and B2

    x + 2y + 3z = 11

    4x – 2y + 2z = 4

    -------------------------(+)

    5x + 5z = 15 --> x = 3 – z

    4) A2 and B1

    2x + 4y + 6z = 22

    2x – y + z = 2

    -------------------------(-)

    5y + 5z = 20 --> y = 4 - z

    Hope this will help. If there is any other thing i can help, dont hesitate to ask.

    Regards,

    Marcellus Tanjaya

    email: bog3lstyle@yahoo.com.sg

    marcellus.tanjaya@gmail.com

  • ?
    Lv 4
    5 years ago

    What you want to do is to bathe up x & y so that they in reality remember upon z. (a million) x + 2y + 3z = 11 (2) 2x - y + z = 2 From (a million) slove x by using transferring something else from left to good (3) x = 11 -2y -3z Use (3) in to modify x in (2) to get the y 2(11 - 2y - 3z) - y + z = 2 => 22 - 5y - 5z = 2 => 20 - 5z = 5y => y = 4 - z (5) (5) in (3) supplies x = 11 - 2(4 - z) - 3z = 3 - z So the reply is x = 3 - z (6) y = 4 - z (7) the position both x & y in reality relies upon on parameter z as requested. to substantiate that the reply is genuine in basic terms insert (6) & (7) in (a million) and (2) to work out that each and every aspect stay equivalent. (6), (7) => (a million) (3 - z) + 2(4 - z) + 3z = 11 -3z + 3z = 11 (6), (7) => (2) 2(3 - z) -(4 - z) + z = 2 -2z +z + z = 2

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