To determine values of (a, b, c) such that the system has infinitely many solutions, we use the property that two linear equations have infinitely many solutions if they are scalar multiples of each other (i.e., they represent the same line).
For the system:
(4x + 6y = 16)
(ax + by = c)
The second equation must be a scalar multiple of the first. The simplest case is when the second equation is identical to the first (scalar multiple of 1).
If (a = 4), (b = 6), (c = 16), the second equation matches the first. Thus, every solution to the first equation is a solution to the second, resulting in infinitely many solutions.
Answer: ((4,6,16))
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