based on the type of equations in the system, what is the greatest possible number of solutions?\n$\begin{cas…

Explanation:

Step1: Identify the equations

The first equation $x^{2}+y^{2}=9$ is a circle with center at the origin $(0,0)$ and radius $r = 3$ (since the general form of a circle equation is $(x - a)^{2}+(y - b)^{2}=r^{2}$, here $a = 0,b = 0,r = 3$). The second equation $9x+2y=16$ can be rewritten as $y=-\frac{9}{2}x + 8$, which is a straight - line equation in slope - intercept form $y=mx + c$ where $m=-\frac{9}{2}$ and $c = 8$.

Step2: Analyze the intersection

The number of solutions of a system of equations is equal to the number of intersection points of the graphs of the equations. A line and a circle can intersect at a maximum of 2 points.

Answer:

B. 2