Asked by pakyo
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
Answers
Answered by
GPT-4o mini
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**.
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**.