1. **Problem statement:** Solve the system of equations $$\begin{cases}(3x+2)(2y-3)=6xy\\(4x+5)(y-5)=4xy\end{cases}$$ 2. **Rewrite each equation:** - First equation: Expand left side $$ (3x+2)(2y-3) = 6xy $$ $$ 6xy - 9x + 4y - 6 = 6xy $$ 3. **Simplify first equation:** Subtract $6xy$ from both sides: $$ \cancel{6xy} - 9x + 4y - 6 = \cancel{6xy} $$ $$ -9x + 4y - 6 = 0 $$ 4. **Rewrite second equation:** $$ (4x+5)(y-5) = 4xy $$ $$ 4xy - 20x + 5y - 25 = 4xy $$ 5. **Simplify second equation:** Subtract $4xy$ from both sides: $$ \cancel{4xy} - 20x + 5y - 25 = \cancel{4xy} $$ $$ -20x + 5y - 25 = 0 $$ 6. **Rewrite simplified system:** $$ \begin{cases} -9x + 4y - 6 = 0 \\ -20x + 5y - 25 = 0 \end{cases} $$ 7. **Solve the system:** Multiply first equation by 5 and second by 4 to align $y$ coefficients: $$ \begin{cases} -45x + 20y - 30 = 0 \\ -80x + 20y - 100 = 0 \end{cases} $$ 8. **Subtract first from second:** $$ (-80x + 20y - 100) - (-45x + 20y - 30) = 0 $$ $$ -80x + 20y - 100 + 45x - 20y + 30 = 0 $$ $$ -35x - 70 = 0 $$ 9. **Solve for $x$:** $$ -35x = 70 $$ $$ x = \frac{70}{-35} = -2 $$ 10. **Substitute $x=-2$ into first simplified equation:** $$ -9(-2) + 4y - 6 = 0 $$ $$ 18 + 4y - 6 = 0 $$ $$ 4y + 12 = 0 $$ $$ 4y = -12 $$ $$ y = -3 $$ 11. **Check solution in original equations:** - Check first: $$ (3(-2)+2)(2(-3)-3) = ( -6 + 2)(-6 - 3) = (-4)(-9) = 36 $$ $$ 6(-2)(-3) = 6 \times -2 \times -3 = 36 $$ - Check second: $$ (4(-2)+5)(-3 - 5) = (-8 + 5)(-8) = (-3)(-8) = 24 $$ $$ 4(-2)(-3) = 24 $$ Both checks are correct. **Final answer:** The solution is $\boxed{(-2;-3)}$ which corresponds to option B.