Solve for x & y

Discussion in 'Algebra' started by nycmathguy, Jul 4, 2022.

  1. nycmathguy

    nycmathguy

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    Solve this system of equations.

    x + xy + y = 11
    (x^2)(y) + x(y^2) = 30
     
    nycmathguy, Jul 4, 2022
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  2. nycmathguy

    MathLover1

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    x + xy + y = 11............eq.1
    (x^2)(y) + x(y^2) = 30..........eq.2

    xy + y = 11-x.............1)
    (x +1) y = 11-x
    y = (11-x)/(x +1)..........substitute in

    (x^2)(y) + x(y^2) = 30.............eq.2

    (x^2)((11-x)/(x +1)) + x((11-x)/(x +1))^2 = 30

    (x (11 - x) (x^2 + 11))/(x + 1)^2 = 30

    x (11 - x) (x^2 + 11)= 30(x + 1)^2

    x (11 - x) (x^2 + 11)= 30(x + 1)^2

    -x^4 + 11 x^3 - 11 x^2 + 121 x=30 x^2 + 60 x + 30

    -x^4 + 11 x^3 - 41 x^2 + 61 x - 30 = 0..........using calculator

    we get x=1, x=2, x=3, x=5

    then

    y = (11-x)/(x +1)=(11-1)/(1 +1)=10/2=5
    y = (11-x)/(x +1)=(11-2)/(2 +1)=9/3=3
    y = (11-x)/(x +1)=(11-3)/(3 +1)=8/4=2
    y = (11-x)/(x +1)=(11-5)/(5 +1)=6/6=1

    solutions:
    x=1, y=5
    x=2, y=3
    x=3, y=2
    x=5, y=1
     
    MathLover1, Jul 4, 2022
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  3. nycmathguy

    nycmathguy

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    Thank you very much. No more monster questions. We will go back to our College Algebra textbook when time allows and when the heatwave goes away. I am moving to my new place on August 7.
     
    nycmathguy, Jul 4, 2022
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