MATH HW PLZ HELP!!!!?

The first one tells me to solve the equation using elimination and/or substitution.

2x - 3y + z = 10

3x - 8y +2z =11

-x + 5y- 3z = 15

The second question is asking to solve the system using Cramer's Rule.

3x - 7y + 4z = 11

x + y - z = 4

2x - 6y + z = 15

Please explain how you got your answers as for i have to show work!

Thank you for all your help =]!

1 Answer

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  • Leltos
    Lv 5
    1 decade ago
    Favorite Answer

    Lets eliminate x first. Take the first 2 equations.

    3 * (2x - 3y + z = 10)

    -2 * (3x - 8y +2z =11)

    => 9y - 16y + 3z - 4z = 30 - 22

    -7y -z = 8

    Now do it with the last 2 equations.

    1 * (3x - 8y +2z =11)

    +3 *(-x + 5y- 3z = 15)

    => -8y + 15y + 2z -9z = 11 + 45

    7y -7z = 56

    You can add the 2 results to cancel y

    -8z = 64

    z = -8

    Subbing in to -7y -z = 8

    -7y - (-8) = 8

    -7y = 0

    y = 0

    Subbing into 2x - 3y + z = 10

    2x - 3*0 + -8 = 10

    2x = 18

    x = 9

    (x,y,z) = (9, 0 -8)

    A quick check shows that this satisfies all the equations (plug them back in all 3 equations to check).

    ==========

    Note, determinant of

    a b c

    d e f

    g h i

    = aei + bfg + cdh - gec - hfa - idb

    x = det(

    11 7 4

    4 1 -1

    15 -6 1)/

    det(

    3 7 4

    1 1 -1

    2 -6 1)

    = -344/-68

    = 86/17

    = 5 1/17 ~ 5.059

    y = 52 / -68

    = -13 / 17

    z = -20/68

    = -5/17

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