Answer :
It is not possible for a system of two quadratic equations to have exactly three solutions. Here's why:
1. When you graph quadratic equations, they form parabolas. These parabolas can intersect at most two points. This is a fundamental property of quadratic functions.
2. Even if you rotate or shift the graphs of the quadratic equations, they will still maintain their basic shape as parabolas and intersect at most two points. Rotations or translations do not change the fact that a quadratic equation can have at most two solutions.
3. Therefore, the statement that a system of two quadratic equations can have exactly three solutions is incorrect based on the nature of quadratic functions and their graphical representation.