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 the general solu an ordered pair in terms of \( x \). Include a multiplication sign between symbols. For example, \( a^{*} x \). (3,-3)

To solve the system of equations: 1. We can use substitution or elimination. Let’s rearrange the second equation: \[ x = 4y - 3. \] 2. Now substitute \( x \) in the first equation: \[ -3(4y - 3) + 12y = 9. \] \[ -12y + 9 + 12y = 9. \] \[ 9 = 9. \] 3. This means any \( y \) value will satisfy this equation, indicating infinite solutions. Now substituting back in terms of \( y \): \[ x = 4y - 3. \] Thus, the general solution is \( (4y - 3, y) \) for any \( y \). Now for some fun snippets about systems of equations: Ever wondered how long people have been solving these? The concept of linear equations and systems has roots dating back to ancient civilizations like the Babylonians, who used a form of algebra to solve problems involving numbers and measurements. They laid the groundwork for much of modern mathematics! If you ever find yourself falling into the trap of mixing signs when adding or subtracting equations, take a moment to double-check your arithmetic. It’s all too easy to slip up there! A good tip is to write each step clearly and even use a different colored pen for different equations—making it visually engaging can help prevent those pesky mistakes!