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X+Y=5XY,3X+2Y=13XY where x and y are not equl to 0

  • MATH -

    3(X+Y=5XY)
    3X+2Y=13XY

    3X+3Y=15XY ------(1)
    3X+2Y=13XY ------(2)
    ----------
    SUBTRACT (1)-(2)
    Y=2XY
    CANCEL Y ON BOTH SIDES
    => 2X=1
    =>X=1/2
    FROM EQUATION --(1)
    3Y=15XY-3X
    3Y=3(5XY-X)
    CANCEL 3
    Y=5XY-X
    =>5XY-Y=X
    =>Y(5X-1)=X -----(3)
    NOW SUBSTITUTE X IN EQUATION ----(3)
    Y(5*(1/2)-1)=1/2
    =>Y[(5/2)-1]=1/2
    =>Y[2.5-1]=0.5
    =>Y[1.5]=0.5
    =>Y[3]=1
    =>Y=1/3

    THEREFORE X=1/2 & Y=1/3

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