How many solutions does the system have? \( \left\{\begin{array}{l}3 y=-6 x+9 \\ y=-6 x+9\end{array}\right. \) Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

To solve the system   {    3y = -6x + 9    y = -6x + 9   } start by rewriting the first equation in slope-intercept form by dividing both sides by 3:   y = (-6/3)x + 9/3   y = -2x + 3 Now the system becomes:   y = -2x + 3   y = -6x + 9 Since these are two linear equations with different slopes (-2 and -6), they represent two distinct non-parallel lines that will intersect exactly once. To find the intersection, set the right-hand sides equal to each other:   -2x + 3 = -6x + 9 Add 6x to both sides:   4x + 3 = 9 Subtract 3 from both sides:   4x = 6 Divide by 4:   x = 6/4 = 3/2 Now plug x = 3/2 into one of the equations (for example, y = -2x + 3):   y = -2(3/2) + 3   y = -3 + 3 = 0 Thus, the intersection point is (3/2, 0). Since the system has a unique solution, the correct answer is: (A) Exactly one solution.