Find $u_1/v$ from the 1st eqn and substitute into the 2nd :
From the 1st equation
where $\mu=m_2/m_1$ which must be $\ge 1$ because $u_1/v \ge 0$.
The 2nd equation can be written as
Substitute for $u_1/v$ :
Therefore $\mu=m_2/m_1=0$ or $3$. We must have $\mu \ge 1$ for realistic solutions so $m_2/m_1=3$ is the only solution.