For Exercises 11–22, use Cramer's Rule to solve each system. x + y = 7 x - y = 3

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1. Step 1: Write the system of equations in matrix form: \(A\mathbf{x} = \mathbf{b}\), where \(A = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}\), \(\mathbf{x} = \begin{pmatrix} x \\ y \end{pmatrix}\), and \(\mathbf{b} = \begin{pmatrix} 7 \\ 3 \end{pmatrix}\).
2. Step 2: Calculate the determinant of matrix \(A\), denoted as \(\text{det}(A)\). For a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\), the determinant is given by \(ad - bc\).
3. Step 3: Form the matrices \(A_x\) and \(A_y\) by replacing the respective columns of \(A\) with the column vector \(\mathbf{b}\). For \(A_x\), replace the first column of \(A\) with \(\mathbf{b}\), and for \(A_y\), replace the second column of \(A\) with \(\mathbf{b}\).
4. Step 4: Calculate the determinants of \(A_x\) and \(A_y\).
5. Step 5: Use Cramer's Rule to find the solutions for \(x\) and \(y\). According to Cramer's Rule, \(x = \frac{\text{det}(A_x)}{\text{det}(A)}\) and \(y = \frac{\text{det}(A_y)}{\text{det}(A)}\).