7 Solve the system with the addition method: \( \left\{\begin{array}{l}-9 x-8 y=-59 \\ 2 x+9 y=42\end{array}\right. \) One solution: Ono solution Onfinite number of solutions

To solve the system using the addition method, first, we want to eliminate one variable by making the coefficients of either \(x\) or \(y\) the same. Let's multiply the second equation by 4, which gives us: \[ \left\{\begin{array}{l}-9x - 8y = -59 \\ 8x + 36y = 168\end{array}\right. \] Now, add both equations together: \[ (-9x + 8x) + (-8y + 36y) = -59 + 168 \Rightarrow -x + 28y = 109. \] Next, isolate \(x\) or \(y\) to find the solution. Now onto another interesting fact: although this method looks easy, it can sometimes lead to confusion over signs or missed numbers. To avoid mistakes, double-check each step as you combine equations. A simple oversight can turn one solution into none!