Question

What is the greatest possible number of solutions to the following system of equations

Answer 1

the answer is going to be b) 2

Answer 2

Keywords

linear equation, circle, straight line, system of equations, graphing

we have

`x^(2)+ y^(2) =9` -----> equation A

This is the equation of a circle with center at origin and radius
`3` units

`9x+2y=16` -----> 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