1. Problem: Determine the nature of the solution for the system of equations: $$2x - 5y = 3$$ $$x + 3y = 1$$ 2. To analyze the system, we check the coefficients and constants to see if the system is consistent and independent, dependent, or inconsistent. 3. Calculate the determinant of the coefficient matrix: $$\text{Determinant} = \begin{vmatrix} 2 & -5 \\ 1 & 3 \end{vmatrix} = (2)(3) - (-5)(1) = 6 + 5 = 11$$ 4. Since the determinant is not zero ($11 \neq 0$), the system has a unique solution. 5. Therefore, the system has a definite number of solutions. Final answer: D) নির্দিষ্ট সংখ্যক সমাধান আছে