Final answer:
The system of equations p^2 + q^2 = 1 and x/3 = y/4 = z/5 consists of a circle equation with many points (p, q) and proportional relationships between x, y, and z with infinite solutions due to lacking constraints.
Step-by-step explanation:
To solve the given system of equations, p^2 + q^2 = 1 and x/3 = y/4 = z/5, we begin by recognizing that the first equation represents a circle with radius 1 on the p-q plane. Since the radius is fixed, there is an infinite number of points (p, q) that satisfy this equation, representing the uniqueness or otherwise of the solution. The second part of the question is a set of proportional relationships between x, y, and z, indicating that they are in a constant ratio. We can express y and z in terms of x by choosing a common variable, such as k, where x = 3k, y = 4k, and z = 5k.
However, without additional information to constrain the values of x, y, and z further, we cannot find unique solutions for these variables. The solution to this system is not unique because there are an infinite number of triples (x, y, z) that satisfy the proportional relationship. Thus, while the equation p^2 + q^2 = 1 uniquely defines a circle, the lack of additional constraints in x/3 = y/4 = z/5 leads to a non-unique solution of infinite possibilities for (x, y, z).