Final answer:
The number of solutions of the given system of equations can be found by expressing x in terms of y from the first equation, substituting into the second, and solving the resulting quadratic equation.
Step-by-step explanation:
The correct answer to the question of finding the number of solutions of the system of equations x + \frac{1}{y} = 2 and 2xy - 3y = -2 requires solving the system simultaneously.
First, manipulate the first equation to express x in terms of y, which gives us x = 2 - \frac{1}{y}. Substituting this expression for x into the second equation will allow us to solve for y, and then back-substitute to find x.
This process can result in a specific number of solutions, which is determined by the resulting quadratic equation from the substitution.