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Math Help - solve equation

  1. #1
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    solve equation

    If x^2-y^2=77 and x+y=11, what is the value of x?
    I don't get why the correct answer is 9. Thanks in advance
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  2. #2
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    Hello,
    Quote Originally Posted by fabxx View Post
    If x^2-y^2=77 and x+y=11, what is the value of x?
    I don't get why the correct answer is 9. Thanks in advance
    Note that 77=x^2-y^2=({\color{red}x+y})(x-y)
    You'll get an equation : (x-y)=... and associated to the x+y=11 one, you'll have a linear system of two equations.
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    But if you do like that, won't you have x in terms of y? I need a value of x with a number. (
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    Quote Originally Posted by fabxx View Post
    But if you do like that, won't you have x in terms of y? I need a value of x with a number. (
    Get the equations first.

    1/ Simplify (x+y)(x-y)=77 thanks to the equation x+y=11. This gives a second equation.
    2/ Write the system x+y=11 and x-y=... and simplify the y's.
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  5. #5
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    Ok, i'll give it a try.
    (x+y)(x-y)=77 and because (x+y)=11 so 11(x-y)=77
    Therefore, 11x-11y=77
    so, x-y=7
    also, from before, x+y=11
    so, I try to get rid of the y
    -2y=-4
    y=2
    sub y=2 into equation
    x+2=11
    so x=9!!

    Thank you so much !! You helped a lot
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    Quote Originally Posted by fabxx View Post
    Ok, i'll give it a try.
    (x+y)(x-y)=77 and because (x+y)=11 so 11(x-y)=77
    Therefore, 11x-11y=77
    so, x-y=7
    also, from before, x+y=11
    so, I try to get rid of the y
    -2y=-4
    y=2
    sub y=2 into equation
    x+2=11
    so x=9!!

    Thank you so much !! You helped a lot
    It is correct ! though long !

    I'll show you how I would do (and I guess it's faster...)

    (x+y)(x-y)=77
    11(x-y)=77
    Divide by 11 :
    x-y=7
    And we had x+y=11.

    Add these two equations term by term, because you have -y and y.
    This gives (x-y)+(x+y)=7+11
    2x=18


    Do you see which steps look simpler ?
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