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 \( x \).

To solve the system of equations: 1. **Equation 1**: \(-3x + 12y = 9\) 2. **Equation 2**: \(x - 4y = -3\) We can start by solving the second equation for \(x\): \[ x = 4y - 3 \] Next, we substitute \(x\) into the first equation: \[ -3(4y - 3) + 12y = 9 \] Now, simplify: \[ -12y + 9 + 12y = 9 \] This simplifies to: \[ 9 = 9 \] This statement is true for all values of \(y\), indicating there are infinitely many solutions. Now we can express the solutions as an ordered pair in terms of \(y\): Substituting \(y\) back into \(x\): \[ (x, y) = (4y - 3, y) \] Thus, the solution can be expressed as the ordered pair: \[(4y - 3, y)\]