Question

Based on the type of equations in the system, what is the greatest possible number of solutions? StartLayout Enlarged left-brace 1st Row x squared + y squared = 9 2nd row 9 x + 2 y = 16 EndLayout

Answer 1

Answer:

2

Step-by-step explanation:

Given the system of equations:

$x^2+y^2=9\\9x+2y=16$

Comparing $x^2+y^2=9$ with the general standard equation of a circle $(x-h)^2+(y-k)^2=r^2$.

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.