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Math Help - Solutions to equations

  1. #1
    Ash
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    Solutions to equations

    Can you show me how to go about solving these problems? I'm suppose to translate the given information into a system of equations and solve the system to determine the two numbers.

    #1. One number exceeds a second number by 8. Three-fourths of the larger number is 3 more than the smaller number.



    With the problem #2, I want to make sure I'm doing it right.
    I'm suppose to determine whether each ordered pair is a solution of the given system of linear equations.

    #2 (-0.5,0)

    2x+3y=3
    8x=12y-4



    When I plug (-0.5,0) into the equation I get

    2(-0.5) + 3(0)=3
    -3 = 3 ,


    8(-0.5) = 12(0)-4
    - 4.0 = 4
    -4 = -4 ,

    So would (-0.5,0) not be a solution to both equations since one 3 is negative and the other is a positive 3? I know it would of been a solution if it was -4 = -4 and the other was 3 = 3, but I'm not sure since one three is negative.
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  2. #2
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    Quote Originally Posted by Ash View Post
    Can you show me how to go about solving these problems? I'm suppose to translate the given information into a system of equations and solve the system to determine the two numbers.

    #1. One number exceeds a second number by 8. Three-fourths of the larger number is 3 more than the smaller number.



    With the problem #2, I want to make sure I'm doing it right.
    I'm suppose to determine whether each ordered pair is a solution of the given system of linear equations.

    #2 (-0.5,0)

    2x+3y=3
    8x=12y-4



    When I plug (-0.5,0) into the equation I get

    2(-0.5) + 3(0)=3
    -3 = 3 ,


    8(-0.5) = 12(0)-4
    - 4.0 = 4
    -4 = -4 ,

    So would (-0.5,0) not be a solution to both equations since one 3 is negative and the other is a positive 3? I know it would of been a solution if it was -4 = -4 and the other was 3 = 3, but I'm not sure since one three is negative.
    #1 Let x and y be the two numbers, assuming that x is the largest.
    Since"One number exceeds a second number by 8. ",
    x=y+8
    the second sentence provides the second equation:"Three-fourths of the larger number is 3 more than the smaller number."
    3/4x=y+3
    solving the system you have the solution: x=20, y=12
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  3. #3
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    #2 You are right, the pair is not a solution .
    Pay attention when evaluating expresion. respect the order of operation. Multiplication first, then addition.
    2(-0.5) + 3(0)=3
    -1+0=3
    -1=3 is not true, so right away you can say that the pair is not a solution.
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  4. #4
    Ash
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    Quote Originally Posted by alinailiescu View Post
    #1 Let x and y be the two numbers, assuming that x is the largest.
    Since"One number exceeds a second number by 8. ",
    x=y+8
    the second sentence provides the second equation:"Three-fourths of the larger number is 3 more than the smaller number."
    3/4x=y+3
    solving the system you have the solution: x=20, y=12
    Thanks for your help, I now see where I went wrong on the second problem, but can you show me the steps in how you came up with x= 20 and y=12 ?
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  5. #5
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    You have the system:
    x=y+8
    3/4x=y+3
    using substitution method, by writting y+8 (from the first equation) insted of x into the second we have:
    3/4(y+8)=y+3
    3/4y+6=y+3
    6-3=y-3/4y
    3=1/4y
    12=y,
    using this value into the first equation we have x=12+8so, x=20
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