Keywords
linear equation, circle, straight line, system of equations, graphing
we have
[tex]x^{2}+ y^{2} =9[/tex] -----> equation A
This is the equation of a circle with center at origin and radius [tex]3[/tex] units
[tex]9x+2y=16[/tex] -----> equation B
This is a linear equation
The system of equations is composed of equation A and equation B
The solution of the system of equations are the intersection points both graphs
we know that
If a straight line intersects a circle the maximum there can be are two points of intersection
Verify
Using a graphing tool
see the attached figure
The number of solutions are two
therefore
the answer is
Two solutions
