1. **Problem statement:** Solve the system of linear equations for part A: $$\begin{cases} 3x - 2y = 7 \\ 7x + 2y = 13 \end{cases}$$ 2. **Formula and rules:** To solve a system of two linear equations, we can use the elimination method by adding or subtracting equations to eliminate one variable. 3. **Step 1: Add the two equations to eliminate $y$:** $$ (3x - 2y) + (7x + 2y) = 7 + 13 $$ $$ 3x + 7x - 2y + 2y = 20 $$ $$ 10x = 20 $$ 4. **Step 2: Solve for $x$:** $$ x = \frac{20}{10} $$ $$ x = 2 $$ 5. **Step 3: Substitute $x=2$ into the first equation to find $y$:** $$ 3(2) - 2y = 7 $$ $$ 6 - 2y = 7 $$ 6. **Step 4: Solve for $y$:** $$ -2y = 7 - 6 $$ $$ -2y = 1 $$ $$ y = \frac{1}{-2} $$ $$ y = -\frac{1}{2} $$ **Final answer:** $$ x = 2, \quad y = -\frac{1}{2} $$