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Math Help - Solving Systems Using Elimination

  1. #1
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    Talking Solving Systems Using Elimination

    I need help solving this problem using elimination

    2x-2y=61
    2x+y=-7

    Please help!!
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  2. #2
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    2x+2y=61 2x+y=7


    2x+2y=61
    -2y -2y
    __________
    2x = 61 - 2y
    ___________
    2 -> divide both sides by 2

    x = 30.5 - y

    put this x value into other equation:

    2(30.5 -y) +y = 7
    61 - 2y + y = 7
    -y -y
    ______________
    61 - 2y = 7 - y
    +2y +2y
    ______________
    61 = 7 + y
    -7 -7
    ______________
    56 = y

    Now substitute 56 for y:

    2x + 2(56) = 61
    2x + 112 = 61
    -2x -61 -61 -2x
    __________________
    51 = -2x
    ________
    -2 -> divide both sides by (-2)
    x = -25.5

    Now put (-25.5) for x and 56 for y to check your answers:

    2(-25.5) + 2(56) = 61
    -51 + 112 = 61
    61 = 61

    =]
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  3. #3
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    Elimination means you eliminate either the x term or the y to term to leave you with just y = or x =.

    As there are 2 xs in both terms, we can subtract the second term from the first to eliminate the xs.

    2x - 2y = 61
    -
    2x + y = -7
    =
    -3y = 68
    y = -22.666...

    Now that you have y, all you need to do is solve the first equation using y as 68.

    So 2x - 2 * -22.6666... = 61
    2x = 15.3333...
    x = 7.6666...

    Very odd answers, but that is correct. The above poster is incorrect as he mistook 2x - 2y = 61 to be 2x + 2y = 61.
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  4. #4
    Member TheMasterMind's Avatar
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    Quote Originally Posted by Bruce View Post
    Elimination means you eliminate either the x term or the y to term to leave you with just y = or x =.

    As there are 2 xs in both terms, we can subtract the second term from the first to eliminate the xs.

    2x - 2y = 61
    -
    2x + y = -7
    =
    3y = 68
    y = 22.666...

    Now that you have y, all you need to do is solve the first equation using y as 68.

    So 2x - 2 * 22.6666... = 61
    2x = 106.3333...
    x = 53.1666...

    Very odd answers, but that is correct. The above poster is incorrect as he mistook 2x - 2y = 61 to be 2x + 2y = 61.
    you have not conducted this properly, as you did not divide by the remaining co-efficient infront of the x...
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  5. #5
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    I realised my mistake. I have edited my post.
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