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Math Help - Simultaneous equations

  1. #1
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    Exclamation Simultaneous equations

    If (2,1) is a solution of the simultaneous equations
    x(square) + xy + ay = b
    2ax + 3y = b

    find the value of a and b.
    Find also the other solution.
    I was able to find out
    a=1
    b=7
    But not the other solution.
    the answer is supposed to be:
    x=-7 and y=7
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  2. #2
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    Quote Originally Posted by Ilsa View Post
    If (2,1) is a solution of the simultaneous equations
    x(square) + xy + ay = b
    2ax + 3y = b

    find the value of a and b.
    Find also the other solution.
    I was able to find out
    a=1
    b=7 <====== OK
    But not the other solution.
    the answer is supposed to be:
    x=-7 and y=7
    1. Plug in the values of a and b into the two equations:

    \left|\begin{array}{rcl}x^2+xy+y&=&7\\2x+3y&=&7\en  d{array}\right.

    2. Determine x from the 2nd equation: x= -\frac32 y+\frac72

    3. Now replace x in the 1st equation by -\frac32 y+\frac72 and solve for y:

    \left(-\frac32 y+\frac72\right)^2+\left(-\frac32 y+\frac72\right) \cdot y + y = 7

    4. Plug in the value of y into the equation at 2. to get the value of x.
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