\( 1 \leftarrow \quad \) Solve the system by the method of your choice. \[ \begin{array}{l}x=6 y+3 \\ -3 x+18 y=-9\end{array} \] Select the correct choice below and, if necessarv, fill in the answ

To solve the system of equations, we can use substitution or elimination. Let's use substitution since \(x\) is already isolated in the first equation. From the first equation, we know that: \[ x = 6y + 3 \] Now we can substitute this expression for \(x\) into the second equation: \[ -3(6y + 3) + 18y = -9 \] Expanding this gives: \[ -18y - 9 + 18y = -9 \] Notice that the \( -18y \) and \( +18y \) terms cancel out: \[ -9 = -9 \] This is a true statement, indicating that the system has infinitely many solutions. We can express the solution in terms of \(y\) as follows: \[ x = 6y + 3 \] for any real number \(y\). In summary, the solution set is: \[ (x, y) = (6y + 3, y) \] where \(y\) is any real number.