The system of a quadratic equation and a linear equation may have how many intersection points?

An equation is a mathematical statement with an 'equal to' symbol between two algebraic expressions that have equal values.

Answer: The system of a quadratic equation and a linear equation can have either 0, 1, or 2 possible intersection points.

Let us go through the explanation to understand the solution.

Explanation:

The quadratic equation needs to be a parabola and a linear equation is a straight line, they may have at most two intersection points. It could also be possible for a straight line and a parabola to have no intersection point, a single point of intersection, but it is not possible to have more than 2 points of intersection.

There are three possible cases:

1. No real solution (happens when they never intersect)
2. One real solution (when the straight line just touches the quadratic)
3. Two real solutions

The graph shows the three different possible solutions of a quadratic and a linear equation.                                               

Therefore, the system of a quadratic equation and a linear equation can have either 0, 1, or 2 possible intersection points.