1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x - 3y = 2 \\ x + 3y = 10 \end{cases}$$ 2. **Formula and method:** We will use the method of addition (elimination) to solve for $x$ and $y$. The goal is to eliminate one variable by adding or subtracting the equations. 3. **Add the two equations:** $$ (2x - 3y) + (x + 3y) = 2 + 10 $$ Simplify the left side: $$ 2x - 3y + x + 3y = 3x + \cancel{-3y + 3y} = 3x $$ Simplify the right side: $$ 2 + 10 = 12 $$ So we have: $$ 3x = 12 $$ 4. **Solve for $x$:** $$ x = \frac{12}{3} $$ Show cancellation: $$ x = \frac{\cancel{12}}{\cancel{3}} = 4 $$ 5. **Substitute $x=4$ into one of the original equations to find $y$:** Use the second equation: $$ 4 + 3y = 10 $$ 6. **Solve for $y$:** $$ 3y = 10 - 4 $$ $$ 3y = 6 $$ $$ y = \frac{6}{3} $$ Show cancellation: $$ y = \frac{\cancel{6}}{\cancel{3}} = 2 $$ 7. **Final answer:** $$ \boxed{(x, y) = (4, 2)} $$ This means the solution to the system is $x=4$ and $y=2$.