Solve the system of equations by any method. \[ -3 x+12 y=9 \] \[ x-4 y=-3 \] Enter the exact answer as an ordered pair, \( (x, y) \) If there is no solution, enter NS. If there is an infinite number of solutions, enter th an ordered pair in terms of \( x \).

Solve the system of equations \( -3x+12y=9;x-4y=-3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-3x+12y=9\\x-4y=-3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}-3x+12y=9\\x=-3+4y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-3\left(-3+4y\right)+12y=9\) - step3: Simplify: \(9=9\) - step4: Calculate: \(\left(x,y\right) = \left(-3+4y,y\right),y \in \mathbb{R}\) - step5: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations has infinitely many solutions. Therefore, the solution is \( (x, y) = (x, y) \) in terms of \( x \).