Question

What is the greatest possible number of solutions to the following system of equations? X^2+y^2=9

9x+2y=16

Answer 1

Ans = 4

Explanation:

Answer 2

For this case we have the following system of equations:

`x ^ 2 + y ^ 2 = 9 9x + 2y = 16`
To answer the question, what we should do is identify the equations:
The first equation is a circle centered on the origin of radius 3.
The second equation is a line with a negative slope.
A circle and a line can intersect a maximum of two times.
Therefore, the system has a maximum of 4 possible solutions because we have two ordered pairs that can be solved.
Answer:
Maximum 4 possible solutions (two ordered pairs)
See attached image of the graphic solution.