Solve the following system of equations using Cramer's Rule: \[ \begin{align*} 2x + 3y &= 7 \\ 4x - y &= 1 \end{align*} \]

Step 1 ：Step 1: Write down the system of equations in matrix form: \[ \begin{bmatrix} 2 & 3 \\ 4 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 1 \end{bmatrix} \]

Step 2 ：Step 2: Calculate the determinant of the coefficient matrix: \[ D = \begin{vmatrix} 2 & 3 \\ 4 & -1 \end{vmatrix} = (2*(-1)) - (3*4) = -10 \]

Step 3 ：Step 3: Form the matrix Dx by replacing the first column of the coefficient matrix with the constants, and calculate its determinant: \[ Dx = \begin{vmatrix} 7 & 3 \\ 1 & -1 \end{vmatrix} = (7*(-1)) - (3*1) = -10 \] and so \[ x = \frac{Dx}{D} = \frac{-10}{-10} = 1 \]

Step 4 ：Step 4: Form the matrix Dy by replacing the second column of the coefficient matrix with the constants, and calculate its determinant: \[ Dy = \begin{vmatrix} 2 & 7 \\ 4 & 1 \end{vmatrix} = (2*1) - (7*4) = -24 \] and so \[ y = \frac{Dy}{D} = \frac{-24}{-10} = 2.4 \]