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- How can one determine the number of solutions of a nonlinear system?

I developed a program to solve the nonlinear system below through the method of successive approximations and was only able to find one solution, namely ##x_1 = 0.93377## and ##x_2 =0.88417##, even though I tried many different starting points. I was wondering if there's a way to determine if there are other solutions to this system, and if so, how many more there would be.

**\begin{cases} 3x_1^2 + x_2 = \frac{7}{2} \\ x_1 + x_2^3 = \frac{13}{8} \end{cases}**
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