4. \( \begin{array}{l}y=-3 x-9 \\ 5 x+2 y=-16\end{array} \)

To solve this system of equations, you can use the substitution or elimination method. Let's take the first equation, \(y = -3x - 9\), and substitute it into the second equation. By substituting, we replace \(y\) in \(5x + 2y = -16\) with \(-3x - 9\): \[ 5x + 2(-3x - 9) = -16 \] This simplifies to: \[ 5x - 6x - 18 = -16 \] which leads to: \[ -x - 18 = -16 \] Thus, solving gives \(x = -2\). Plug this \(x\) back into the first equation to find \(y\): \[ y = -3(-2) - 9 = 6 - 9 = -3 \] The solution to the system is \(x = -2\) and \(y = -3\). --- Now, if you've ever wondered about the art of solving systems, think of it as a puzzle! Each equation is like a clue, leading you closer to the treasure—an intersection point. Play around with different methods, and soon, you'll find your own shortcuts to solving any system of equations efficiently! When tackling equations, a common blunder is forgetting to distribute or combine like terms correctly. Double-check your work; a tiny math mishap can lead you down a dead-end road! Always recalibrate your calculations—a healthy habit that will keep your math skills sharp and reliable!