This solution will detail the conditions for a system of linear equations to have a unique solution, no solution, or infinitely many solutions, and then apply these concepts to analyze each given option.

Key Concepts for Systems of Linear Equations (Cramer's Rule)

For a system of linear equations in three variables: $a_1x + b_1y + c_1z = d_1$ $a_2x + b_2y + c_2z = d_2$ $a_3x + b_3y + c_3z = d_3$ We define the determinant of the coefficient matrix, $\Delta$, and the determinants $\Delta_x, \Delta_y, \Delta_z$ by replacing the respective coefficient columns