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Math Help - Systems of nonlinear equations in two variables

  1. #1
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    Systems of nonlinear equations in two variables

    Can you please check my answers?

    Solve the system by the substitution method.

    -12x-y=22
    y=x^2+10

    answer: {(-8,74), (-4,260)}

    x+y=8
    y=x^2-4x+4

    answer: {(4,4), (-1,9)}

    y=x-4
    y^2=-16x

    answer: {(-4,-8)}

    x^2+y^2=41
    x+y=9

    answer: {(5,4),(4,5)}

    Solve the system by the substitution method.

    x^2+y^2=36
    x^2-y^2=36

    answer: {(6,0), (-6,0)}

    7x^2+y^2=49
    7x^2-y^2=49

    answer:{(square root 7,0), (negative square root 7,0)}

    x^2+y^2=4
    4x^2+9y^2=36

    answer: {(0,2),(0,-2)}

    x^2-y^2=25
    4x^2+25^2=100

    answer: {(5,0), (-5,0)}
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by soly_sol View Post
    Can you please check my answers?

    Solve the system by the substitution method.

    -12x-y=22
    y=x^2+10

    answer: {(-8,74), (-4,260)}
    I assume this is a typo: the second pair is (-4, 26).

    Quote Originally Posted by soly_sol View Post
    x+y=8
    y=x^2-4x+4

    answer: {(4,4), (-1,9)}

    y=x-4
    y^2=-16x

    answer: {(-4,-8)}

    x^2+y^2=41
    x+y=9

    answer: {(5,4),(4,5)}

    Solve the system by the substitution method.

    x^2+y^2=36
    x^2-y^2=36

    answer: {(6,0), (-6,0)}

    7x^2+y^2=49
    7x^2-y^2=49

    answer:{(square root 7,0), (negative square root 7,0)}

    x^2+y^2=4
    4x^2+9y^2=36

    answer: {(0,2),(0,-2)}

    x^2-y^2=25
    4x^2+25^2=100

    answer: {(5,0), (-5,0)}
    These are all good. (In the last problem, I presume the second equation is really 4x^2 + 25y^2 = 100.

    -Dan
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