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

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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To solve the given system of equations, you can use the method of substitution or elimination. I will explain how to solve it using substitution.

1. Start with the first equation:
X + Y = 5XY

2. Solve this equation for one variable in terms of the other. Let's solve for X:
X = 5XY - Y

3. Now substitute this expression for X in the second equation:
3(5XY - Y) + 2Y = 13XY

4. Simplify and solve for Y:
15XY - 3Y + 2Y = 13XY
15XY - Y = 13XY
15XY - 13XY = Y
2XY = Y

5. Now, substitute the value of Y back into the first equation to solve for X:
X + 2XY = 5XY
X = 5XY - 2XY
X = 3XY

6. We have now expressed both X and Y in terms of XY. But we want the actual values of X and Y, not in terms of XY. To do that, we need an additional equation with the variable XY.

7. At this point, we can substitute either X or Y in one of the original equations with 3XY. Let's substitute X in the first equation:
(3XY) + Y = 5XY
3XY + Y = 5XY

8. Simplifying this equation, we get:
Y = 2XY

9. Now, substitute this value of Y back into the equation X = 3XY:
X = 3(2XY)
X = 6XY

10. Finally, we have two equations, Y = 2XY and X = 6XY, where both variables are expressed in terms of XY.

To find the value of X and Y, we need more information or an additional equation that involves one of these variables directly. Without this additional information, it is not possible to find the specific values of X and Y.