Solving the system of equations using the elimination method:

Step 1: Rearrange the equations
- Multiply the second equation by 2 to make the coefficients of y the same in both equations:
- 6x - 3y = 5xy
- 8x - 6y = 6xy

Step 2: Eliminate a variable
- Subtract the first equation from the modified second equation to eliminate y:
- (8x - 6y) - (6x - 3y) = 6xy - 5xy
- 2x - 3y = xy

Step 3: Solve for x or y
- Substitute the expression for y from the eliminated equation back into one of the original equations to solve for x:
- 6x - 3(2x - 3y) = 5x(2x - 3y)
- 6x - 6x + 9y = 10x^2 - 15xy
- 9y = 10x^2 - 15xy

Step 4: Substitute x back into the equations
- Plug the value of x back into one of the original equations to solve for y:
- 6(1) - 3y = 5(1)y
- 6 - 3y = 5y
- 6 = 8y
- y = 3/4

Step 5: Find the value of x
- Substitute the value of y back into one of the equations to find x:
- 6x - 3(3/4) = 5(3/4)x
- 6x - 9/4 = 15/4x
- 6x - 15/4x = 9/4
- 24x - 15x = 9
- 9x = 9
- x = 1

Therefore, the solution to the system of equations is x = 1 and y = 3/4.

6x-4x-3y+3y=3xy-5xy
2x=-2xy