Find the solution of the system of equations. \[ \begin{aligned}-10 x-y & =27 \\ -4 x-y & =9\end{aligned} \]

To solve the system of equations, we can use the method of elimination or substitution. Let's use elimination in this case. We have the following equations: 1) \(-10x - y = 27\) 2) \(-4x - y = 9\) First, we'll eliminate \(y\) by subtracting the second equation from the first: \[ (-10x - y) - (-4x - y) = 27 - 9 \] This simplifies to: \[ -10x + 4x = 18 \implies -6x = 18 \] Now, solve for \(x\): \[ x = \frac{18}{-6} = -3 \] Next, substitute \(x = -3\) into one of the original equations to find \(y\). We'll use the second equation: \[ -4(-3) - y = 9 \] This simplifies to: \[ 12 - y = 9 \implies -y = 9 - 12 \implies -y = -3 \implies y = 3 \] Thus, the solution to the system of equations is: \[ (x, y) = (-3, 3) \]