Respuesta :
Answer:
2
Step-by-step explanation:
Given the system of equations:
[Tex]x^2+y^2=9\\9x+2y=16[/tex]
Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].
The first equation is an equation of a circle centred at (0,0) with a Radius of 3.
The second equation 9x+2y=16 is a straight line equation.
A straight line can only intersect a circle at a maximum of 2 points.
Therefore the greatest possible number of solutions to the equations in the system is 2.
