A system of two linear equations can have the following types of solutions:
1. Unique solution (one solution): This occurs when the two lines intersect at exactly one point. This is the case when the slopes of the two lines are different.
2. No solution: This occurs when the lines are parallel and do not intersect at any point. This happens when the slopes of the two lines are equal, but the y-intercepts are different.
3. Infinite solutions: This occurs when the two lines are coincident, meaning they are the exact same line. In this case, every point on one line is also a point on the other line. This happens when both the slopes and y-intercepts of the two lines are the same.
It is not possible for a system of two linear equations to have exactly two solutions. A system can only intersect at one point (unique solution), not intersect at all (no solution), or coincide completely (infinite solutions).
Therefore, the number of solutions that is not possible for a system of two linear equations is:
A. 2
