A system of equations consisting of a linear equation and a quadratic equation ____ has two solutions.

a. always
b. sometimes **
c. never
Can someone check this

better

One

To determine whether a system of equations consisting of a linear equation and a quadratic equation has two solutions, we need to consider the possible scenarios.

When we graph both equations, we look for the points where the two graphs intersect. If there are two points of intersection, it means that the system of equations has two solutions. However, the possible scenarios are as follows:

1. The linear equation and the quadratic equation intersect at two distinct points: In this case, the system of equations has two solutions. So, option B (sometimes) is correct.

2. The linear equation and the quadratic equation have one point of intersection: This scenario occurs when the linear equation is a tangent to the quadratic equation's graph. In this case, the system has only one solution.

3. The linear equation and the quadratic equation do not intersect: In this scenario, the system of equations has no solutions.

Therefore, the correct answer is option B, sometimes.