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Answer:

A general  line can be represented as , y= m x + c

And general equation of circle is , ax²+by²+2 g x +2 f y +c=0

Now there are following possibilities

1. A line and circle have no common point of intersection, that is no solution.

2. A line may be a tangent to a circle, that is one common point, one solution.

3. A line may intersect a circle maximum at two points, that is 2 solution.

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You can use the definition of the solution to a system of equation to know how the solutions to the given system will come.

There are three cases for the given case's solutions:

No solution, one solution or two solutions.

What are the solution(s) to a system of equations?

Solution to a system of equations are those values to variables which satisfy all the equations in that system simultaneously.

Graphically, those points where all the given equations' graphs intersect is the solution since it lies on all the equation of that system, thus satisfying all the equations of that system.

How to find the solution to the given system of equations?

We know that either a straight line will pass far from the circle(no intersection, thus, no solutions),

or, the line will just touch the circle from outside( tangent, only one point common so one solution).

or, the line will intersect the circle and will divide it in two parts(thus, two points in common, therefore two solutions).

Refer to the diagram for more details.

Thus, there are three cases:

  • No intersection, no solution.
  • One intersection, the line is tangent. Thus, one solution to the system of equations given.
  • Two intersection, the line cuts the circle in two parts. Thus, two solutions to the given system of equations.

Learn more about solutions to system of equations here:

https://brainly.com/question/2825832

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