Solve. \[ \begin{array}{l}x+6 y=-9 \\ 6 x+3 y=12\end{array} \]

To solve the system of equations: 1. \( x + 6y = -9 \) 2. \( 6x + 3y = 12 \) Let's start with the first equation and express \( x \) in terms of \( y \): From equation (1): \[ x = -9 - 6y \] Now, substitute \( x \) from this equation into the second equation (2): \[ 6(-9 - 6y) + 3y = 12 \] Now distribute the \( 6 \): \[ -54 - 36y + 3y = 12 \] Combine like terms: \[ -54 - 33y = 12 \] Next, add \( 54 \) to both sides: \[ -33y = 12 + 54 \] \[ -33y = 66 \] Now, divide both sides by \( -33 \): \[ y = -2 \] Now that we have \( y \), we can substitute it back into the first equation to find \( x \): \[ x + 6(-2) = -9 \] \[ x - 12 = -9 \] Add \( 12 \) to both sides: \[ x = -9 + 12 \] \[ x = 3 \] Thus, the solution to the system of equations is: \[ (x, y) = (3, -2) \]