1. The problem is to solve a system of linear equations using the elimination method. 2. The elimination method involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other. 3. Suppose the system is: $$\begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases}$$ 4. Multiply one or both equations by constants so that the coefficients of one variable are opposites. 5. Add the equations to eliminate that variable: $$\cancel{a_1}x + b_1y = c_1 \\ -\cancel{a_1}x + b_2'y = c_2'$$ 6. Solve the resulting single-variable equation for $y$: $$ (b_1 + b_2')y = c_1 + c_2' $$ 7. Substitute the value of $y$ back into one of the original equations to solve for $x$. 8. This method simplifies solving systems by reducing two variables to one step by step.