Solve the system: \[ \begin{array}{c}-x+3 y=-6 \\ 2 x+2 y=-4\end{array} \]

Let's solve the system of equations: 1. The first equation is: \[ -x + 3y = -6 \] Rearranging it, we get: \[ x = 3y + 6 \] 2. The second equation is: \[ 2x + 2y = -4 \] We can simplify it by dividing everything by 2: \[ x + y = -2 \] Rearranging it, we have: \[ x = -2 - y \] Now we have two expressions for \(x\): - From the first equation, \(x = 3y + 6\) - From the second equation, \(x = -2 - y\) Setting these equal to each other: \[ 3y + 6 = -2 - y \] Now, let's solve for \(y\): 1. Add \(y\) to both sides: \[ 3y + y + 6 = -2 \] \[ 4y + 6 = -2 \] 2. Subtract 6 from both sides: \[ 4y = -2 - 6 \] \[ 4y = -8 \] 3. Divide by 4: \[ y = -2 \] Now that we have \(y\), we can substitute it back to find \(x\): Using \(x = -2 - y\): \[ x = -2 - (-2) = -2 + 2 = 0 \] Thus, the solution to the system of equations is: \[ (x, y) = (0, -2) \]