Question

Based on the type of equations in the system, what is the greatest possible number of solutions?

Answer 1

Answer:

Greatest possible number of solutions of these set of equations are 2

Step-by-step explanation:

We have been given two functions in the question.

x² + y² = 9

9x + 2y = 16

We know that the equation of circle is given by:

(x - h)² + (y - k)² = r²

However, if (h, k) is equals to (0, 0), the equation of circle becomes:

x² + y² = r²

Which is similar to the fist equation

x² + y² = 3²

Hence first equation is a circle.

As the second equation is a linear equation, it is simply a line.

We know that a line passing through the circle can intersect it at only 2 points.

Where points of intersection between both circle and line shows the solution.

So.

There are 2 possible solution to this set of equations