1. **Problem statement:** Solve the system of linear equations: $$\begin{cases} x + 2y = 4 \\ -x + 4y = 2 \end{cases}$$ 2. **Formula and method:** We will use the method of addition (elimination) to solve the system. The goal is to eliminate one variable by adding the two equations. 3. **Step 1: Add the two equations** $$ (x + 2y) + (-x + 4y) = 4 + 2 $$ Simplify: $$ x - x + 2y + 4y = 6 $$ $$ 6y = 6 $$ 4. **Step 2: Solve for $y$** $$ y = \frac{6}{6} = 1 $$ 5. **Step 3: Substitute $y=1$ into the first equation** $$ x + 2(1) = 4 $$ $$ x + 2 = 4 $$ $$ x = 4 - 2 = 2 $$ 6. **Final answer:** $$ x = 2, \quad y = 1 $$ This means the solution to the system is the point $(2,1)$ where both equations intersect.