algebra

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well i'm stumped. i can't figure out how to solve this.
solve for (x,y):
3/x + 2/y = 0
5/x - 1/y = 13
i can't graph it, and i can't use a calculator. i keep getting stuck on the second equation b/c i get 5y -13xy -x=0 and since 13 is a prime number i cant figure out what to do next.

  • algebra -

    first:
    3/x + 2/y = 0
    times xy
    3y + 2x = 0
    y = -2x/3

    in 2nd:
    times xy
    5y - x = 13xy
    sub in y = -2x/3
    5(-2x/3) - x = 13x(-2x/3)
    -10x/3 - x = -26x^2/3
    times 3
    -10x - 3x = -26x^
    26x^2 - 13x = 0
    13x(2x - 1) = 0
    x = 0 or x = 1/2
    but x cannot be zero or else we divided by zero in each equation, that would be undefined

    x = 1/2
    then y = (-2/3)(1/2) = -1/3

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