Algebra

1. I need help solving the system by substitution
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

asked by Samantha
  1. get rid of y so you can use the third eqn

    y = 8-x-z
    so
    -4x + 4(8-x-z) + 5z = 7
    -8 x + z + 32 = 7
    -8x + z = -25 and we know
    +2x +2z = 4

    -16x +2z =-50
    + 2x +2z = 4
    ---------------
    -18 x = -54
    x = 3
    now go back

    posted by Damon
  2. let's clean them up a bit first
    -x-y-z=-8 ---> x + y + z = 8 , #1
    2x+2z=4 ----> x + z = 2 , #3

    how about subtracting those two:
    y = 6 , well that is a good start

    let's put that into #1
    x + 6 + z = 8
    x + z = 2 , but that is what the original #3 said, so we have nothing new.

    but let's change that to z = 2-x and put that data into #2

    -4x + 24 + 5(2-x) = 7
    -4x + 24 + 10 - 5x = 7
    -9x = -27
    x = 3
    then z = 2-3 = -1

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

    posted by Reiny
  3. well, we both used elimination at one point or another, going back a bit we had

    -8x + z = -25 and we know
    +2x +2z = 4

    so use z = 8x -25 to substitute in the last one
    2x +2(8x-25) = 4
    18 x -50 = 4
    18 x = 54
    x = 3 again, whew !


    posted by Damon
  4. You said to use substitution but there is no practical reason not to use elimination and I did so automatically for the second half of the problem, sorry.

    posted by Damon
  5. Thank you very much Reiny for showing me the proper steps. and Thank you too Damon for trying to help me.

    posted by Samantha

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