\frac{dx_{1}}{dt} = \left(1 \cdot k_{7} \cdot k_{1} + -1 \cdot k_{7} \cdot k_{2} \cdot x_{1} + -1 \cdot k_{7} \cdot k_{3} \cdot x_{1} \cdot x_{2}\right) / k_{7}\\
\frac{dx_{2}}{dt} = \left(1 \cdot k_{7} \cdot k_{4} \cdot k_{3} \cdot x_{1} \cdot x_{2} + -1 \cdot k_{7} \cdot \left(k_{2} + k_{5}\right) \cdot x_{2}\right) / k_{7}