Final answer:
The statement regarding the system of equations having at least one solution is false, as the determinant (ad-bc) must not be zero for a guaranteed unique solution.
Step-by-step explanation:
The statement that the system of equations ax+by=1; cx+dy=1 has at least one solution regardless of the values of a, b, c, and d is false. To determine whether a system of linear equations has a solution, you must consider the determinant of the system's coefficient matrix, which is ad - bc. If the determinant is zero (when ad equals bc), the system may have either no solution or infinitely many solutions, but we cannot guarantee at least one unique solution in every case. This situation corresponds to the lines being either parallel (no solution) or the same line (infinitely many solutions). Otherwise, if the determinant is not zero, the system will have exactly one unique solution.