Question

With unique examples of your own let’s discuss the number of solutions possible (0, 1, 2, 3, 4) to a system of equations that include a conic section.

Answer 1

The number of solutions possible to a system of equations that include a conic section depends on the type of equations involved

How to determine the number of solutions?

A system of equation that has a conic section may or may not have solutions.

It would have a solution if the equations intersect, when plotted on a graph and it would not, if otherwise

A conic section can be any of:

• Parabola
• Ellipse
• Hyperbola
• Circle

Example 1: No solution

Consider the following system of equations

• y = x² - 10 --- parabola equation
• (x - 1)² + (y - 2)² = 5 --- circle

The above system of equations has no solution because they do not intersect when plotted on a graph (see graph 1)

Example 2: One solution

Consider the following system of equations

• x = 2 --- linear equation
• y = x² - 10 --- parabola

The above system of equations has one solution because they intersect at one point (see graph 2)

Example 3: One solution

Consider the following system of equations

• y = 2x + 1 --- linear equation
• y = x² - 10 --- circle

The above system of equations has two solutions because they intersect at two points (see graph 3)

The above examples imply that a system of equations that involves conic section can have as many solutions as possible.

The number of solutions depends on the type of equations involved

The attached graphs illustrate how a system of equations can have 0 to 4 solutions

Read more about system of equations at:

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