Final answer:
The equation that can create an inconsistent system when paired with x - 2y = 5 is 2x - 4y = 3 (option a) herefore, the correct answer is: Option (a): 2x − 4y = 3
Step-by-step explanation:
The question presented asks which equation can create an inconsistent system when paired with x - 2y = 5. An inconsistent system is one where the two equations do not intersect, meaning they are parallel and have no solutions in common.
We can identify a parallel equation by looking for a situation where the ratios of the coefficients of x and y are equal while the constant terms are different. Option (a) 2x − 4y = 3 has coefficients that are exactly double those of the first equation, suggesting they might be parallel.
However, when checking the constant, it is not a multiple of the original equation's constant, making this the inconsistent pair we are looking for. Options (b), (c), and (d) either do not have proportional coefficients or have constants that could allow for intersections, making them consistent or dependent systems.