7) \( \begin{array}{l}9 x+3 y=-18 \\ 3 x+y=-6\end{array} \)

We are given the system of linear equations: \[ \begin{cases} 9x + 3y = -18 \\ 3x + y = -6 \end{cases} \] Let's solve this system step-by-step. ### Step 1: Simplify the Equations Observe that the first equation can be obtained by multiplying the second equation by 3: \[ 3(3x + y) = 9x + 3y = -18 \] So, the system becomes: \[ \begin{cases} 9x + 3y = -18 \\ 9x + 3y = -18 \end{cases} \] ### Step 2: Analyze the System Since both equations are identical, they represent the same line. This means there are **infinitely many solutions** to this system, and all solutions lie on the line defined by the equation \(3x + y = -6\). ### Step 3: Express the Solution We can express \(y\) in terms of \(x\): \[ 3x + y = -6 \\ y = -3x - 6 \] ### Conclusion **All real numbers \(x\) and \(y\) that satisfy \(y = -3x - 6\) are solutions to the system.** Therefore, the system has infinitely many solutions given by: \[ y = -3x - 6 \quad \text{for any real number } x. \]