1. **State the problem:** Solve the simultaneous equations by elimination method. 2. **General idea:** The elimination method involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other. 3. **Example:** Consider the system: $$\begin{cases} 2x + 3y = 8 \\ 4x - y = 2 \end{cases}$$ 4. **Step 1:** Multiply the second equation by 3 to align the coefficients of $y$: $$4x - y = 2 \implies 12x - 3y = 6$$ 5. **Step 2:** Add the first equation and the modified second equation: $$ (2x + 3y) + (12x - 3y) = 8 + 6 $$ $$ 14x = 14 $$ 6. **Step 3:** Solve for $x$: $$ x = \frac{14}{14} = 1 $$ 7. **Step 4:** Substitute $x=1$ into one of the original equations, e.g., $2x + 3y = 8$: $$ 2(1) + 3y = 8 $$ $$ 2 + 3y = 8 $$ $$ 3y = 6 $$ $$ y = 2 $$ 8. **Final answer:** The solution to the system is: $$ (x, y) = (1, 2) $$ This method works by eliminating one variable to solve for the other, then back-substituting to find the eliminated variable.