1. **State the problem:** Solve the system of linear equations: $$\begin{cases}7x + 2y = 24 \\ 8x + 2y = 30\end{cases}$$ 2. **Subtract the first equation from the second to eliminate $y$: ** $$ (8x + 2y) - (7x + 2y) = 30 - 24 $$ $$ 8x - 7x + \cancel{2y} - \cancel{2y} = 6 $$ $$ x = 6 $$ 3. **Substitute $x=6$ into the first equation to find $y$: ** $$ 7(6) + 2y = 24 $$ $$ 42 + 2y = 24 $$ 4. **Isolate $y$: ** $$ 2y = 24 - 42 $$ $$ 2y = -18 $$ 5. **Divide both sides by 2: ** $$ y = \frac{-18}{2} $$ $$ y = -9 $$ **Final answer:** $$ (x, y) = (6, -9) $$ This solution means the two lines intersect at the point $(6, -9)$.