Answer: The system of a quadratic equation and a linear equation may have: no intersections points, one intersection point or two intersection points.
Explanation:
It is important to remember that when we graph a linear equation, we get a line and when we graph a quadratic equation, we get a parabola.
Then, given a system of a quadratic equation and a linear equation, there are three possibles cases for the solution:
- If the line and the parabola never intersect, then there is no real solution.
- If the line just touches the parabola, then there is one real solution.
- If the line and the parabola intersect at two points, then there Two real solutions.
Then the system of a quadratic equation and a linear equation may have: no intersections points, one intersection point or two intersection points.