Determine the number of reasonable solutions there can be in a system of equations containing one linear equation and one quadratic equation.(1 point) Responses 0, 1, or 2 solutions 0, 1, or 2 solutions 0 solutions 0 solutions 1 solution 1 solution 2 solutions 2 solutions

Answer 1

In a system containing one linear equation and one quadratic equation, there can be a few different scenarios regarding the number of solutions:

1. 0 solutions: This occurs if the linear equation and the quadratic do not intersect at all. For example, if the linear equation represents a line above or below a parabola that opens upwards or downwards without touching it.

2. 1 solution: This can happen if the linear equation is tangent to the quadratic equation, meaning they touch at exactly one point.

3. 2 solutions: This occurs when the linear equation intersects the quadratic equation at two distinct points.

Thus, the total number of reasonable solutions can be 0, 1, or 2 solutions.

Therefore, the correct response is: 0, 1, or 2 solutions.