Consider the system { ax + by = c ; 2ax + 2by = 2c } for nonzero values: a, b, and c. Determine what the set of solutions will be and explain your results in terms of ordered pairs and lines.

• A. Exactly one ordered pair solves both equations because the second is a scaled version of the first, but they still intersect at a single unique point
• B. Two ordered pairs solve the system because linear dependence always yields two solutions corresponding to sign-changed coordinates of a base solution
• C. No ordered pairs solve the system because scaling creates conflicting constraints unless a, b, and c are all zero, so the system is typically inconsistent
• D. Infinitely many ordered-pair solutions: the two equations are dependent and represent the same line, so any (x, y) on ax + by = c is a solution

Answer: (D)