Modular Root II

Number Theory Level 5

\[\begin{align} \begin{cases} x^2 + 3x - 7 &\equiv 0 \pmod{71} \\ x^2 - 5x - 16 &\equiv 0 \pmod{89} \end{cases} \end{align} \]

Let \(x\) be a positive integer satisfying the system of equations above. What is the least possible value of \(x?\)