Solve the system by substitution -x-y-z=-8 -4x+4y+5z=7 2x+2z=4 show the work

Question

Solve the system by substitution
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

show the work

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Answers ( No )

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    2021-11-23T18:29:09+00:00

    ANSWER

    x=3,y=6,z=-1

    EXPLANATION

    We the have the equations,

    -x-y-z=-8

    Multiplying through by negative one gives,

    x+y+z=8---(1)

    Also

    -4x+4y+5z=7---(2)

    and

    2x+2z=4

    Dividing through by 2 gives

    x+z=2

    Making z the subject  gives,

    z=2-x---(3)

    Now we substitute equation (3) into equation (1) and (2)

    Equation (3) in to equation (1) gives,

    x+y+2-x=8

    This implies that;

    y=8-2

    y=6

    We now put equation (3) in (2) to get,

    -4x+4y+5(2-x)=7

    This implies that

    -4x+4y+10-5x=7

    -9x+4y=7-10

    -9x+4y=-3

    But

    y=6

    So,

    -9x+4(6)=-3

    -9x+24=-3

    -9x=-3-24

    -9x=-27

    Dividing through by negative 9 gives

    x=3

    and

    z=2-3

    z=-1

    Therefore x=3,y=6,z=-1

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