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Math Help - Simultaneous equations

  1. #1
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    Simultaneous equations

    Am I correct in thinking that the solutions of x and y in these simultaneous equations

    y - 3x = 4
    x^2 + y^2 = 34

    are x = -1.5 and y = -0.5
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  2. #2
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    Quote Originally Posted by Natasha1 View Post
    Am I correct in thinking that the solutions of x and -0.5+y in these simultaneous equations

    y - 3x = 4
    x^2 + y^2 = 34

    are x = -1.5 and y = -0.5
    No if you put them into the 2nd equation you get

    \displaystyle \left( -\frac{3}{2}\right)^2+\left( -\frac{1}{2}\right)^2=\frac{10}{4} \ne 34

    How did you get this solution?
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  3. #3
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    No. Your solutions do not satisfy the second equation.
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  4. #4
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    By sustitution
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  5. #5
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    No, for if you put those values into the second equation you won't get an answer of 34. What was your working?

    From eq1: y = 4+3x

    You can sub that into eq2 to give a quadratic in x: x^2+(4+3x)^2 = 34

    Eventually you can simplify that down to (5x-3)(x+3) = 0
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  6. #6
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    I did this call equ1 -3x + y = 4 and equ2 x^2 + y^2 = 34

    By squaring all of equ1 you get 9x^2 + y^2 = 16 call that equ3

    Equ3 - equ2 is = to 9x^2 - x^2 + y^2 - Y^2 = 16 - 34 which simplifies to 8x^2 = -18 which brakes down to x = -3/2

    when I sustitute x = -3/2 back into say equ1 i get y = -1/2
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  7. #7
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    I get this

    x^2 + (4 + 3x)^2 -34 = 0
    x^2 + 9x^2 + 24x + 16 -34 = 0
    10x^2 + 24x -18 = =0
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  8. #8
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    Quote Originally Posted by Natasha1 View Post
    I did this call equ1 -3x + y = 4 and equ2 x^2 + y^2 = 34

    By squaring all of equ1 you get 9x^2 + y^2 = 16 call that equ3. e^(i*pi): You don't get that you would get (-3x+y)(-3x+y) = 9x^2-6xy+y^2

    Equ3 - equ2 is = to 9x^2 - x^2 + y^2 - Y^2 = 16 - 34 which simplifies to 8x^2 = -18 which brakes down to x = -3/2

    when I sustitute x = -3/2 back into say equ1 i get y = -1/2
    10x^2 + 24x -18 =0
    I got that. If you divide through by 2 you'll find it factors nicely (although no reason why you can't use the formula)
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  9. #9
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    I see, I just made it far too complicated. Thanks for the help, you are seriously clever guys!
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