Solve the system. Use any method you wish. List all the solutions. Select the correct choice below and fill in any answer boxes in your choice. \( \begin{array}{l}\text { A. The solution(s) is/are } \\ 3 x^{2}+y^{2}=9\end{array} \) (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no solution.

The equation \( 3x^2 + y^2 = 9 \) represents an ellipse centered at the origin. To find solutions, we can rewrite the equation in terms of \( y \): \[ y^2 = 9 - 3x^2 \] This implies \( y = \pm \sqrt{9 - 3x^2} \). The values of \( x \) must satisfy \( 9 - 3x^2 \geq 0\), or \( x^2 \leq 3 \). Hence, the real solutions for \( x \) are in the interval \( [-\sqrt{3}, \sqrt{3}] \). Thus, for any \( x \) in this range, you can find corresponding \( y \) values, creating a set of solutions in the form of ordered pairs \((x, y)\). Examples include \((0, 3)\), \((0, -3)\), \((\sqrt{3}, 0)\), and other points along the ellipse within the specified range for \( x\). So the solution(s) is/are: \((\sqrt{3}, 0), (-\sqrt{3}, 0), (0, 3), (0, -3),\) and so forth, covering various values of \( x \) in the specified range and computing the respective \(y\) values accordingly.