1. Problem: Solve the system of equations using the addition (sudėties) method for part (a): $$\begin{cases} x + 2y = 13 \\ -x + y = 5 \end{cases}$$ 2. Formula and rules: The addition method involves adding or subtracting equations to eliminate one variable. 3. Add the two equations: $$ (x + 2y) + (-x + y) = 13 + 5 $$ $$ \cancel{x} + 2y - \cancel{x} + y = 18 $$ $$ 3y = 18 $$ 4. Solve for $y$: $$ y = \frac{18}{3} = 6 $$ 5. Substitute $y=6$ into the first equation: $$ x + 2(6) = 13 $$ $$ x + 12 = 13 $$ $$ x = 13 - 12 = 1 $$ 6. Final answer: $$ x = 1, \quad y = 6 $$ This completes the solution for the first system using the addition method.