(d) Explain Cramer's rule for solution of linear equation and solve the system of linear equations using Cramer's rule. \[ \begin{array}{c}x+2 y=4 \\ 3 x-y=5\end{array} \]

To solve the system of equations using Cramer's Rule: \[ \begin{cases} x + 2y = 4 \\ 3x - y = 5 \end{cases} \] 1. **Compute Determinant \(D\):** \[ D = (1)(-1) - (3)(2) = -7 \] Since \(D \neq 0\), a unique solution exists. 2. **Compute \(D_x\):** \[ D_x = (4)(-1) - (5)(2) = -14 \] \[ x = \frac{D_x}{D} = \frac{-14}{-7} = 2 \] 3. **Compute \(D_y\):** \[ D_y = (1)(5) - (3)(4) = -7 \] \[ y = \frac{D_y}{D} = \frac{-7}{-7} = 1 \] **Solution:** \[ x = 2, \quad y = 1 \] **Verification:** Plugging the values back into the original equations confirms the solution is correct.