Final answer:
The correct equivalent set of equations to the original pair is option (c): 10x + 20y = 30 and x - 4y = 8, as it scales both equations by the same factor without changing the solution set.
Step-by-step explanation:
To determine which set of equations are equivalent to the given pair of linear equations 2x + 4y = 6 and x - 4y = 8, we need to look for an option where the equations have been manipulated algebraically without changing the solution set.
Option (a) doubles the first equation, yielding 4x + 8y = 12 which is not equivalent because the second equation has not been similarly scaled.
Option (b) introduces an inconsistent scaling factor between the two equations, which doesn't match the original pair.
Option(c) scales both equations by 5, resulting in 10x + 20y = 30 and the second equation remains unchanged, making this the correct answer.
Option (d) mismatches the scaling between the two equations, so it cannot be correct.
Therefore, the correct equivalent set of equations is option (c): 10x + 20y = 30 and x - 4y = 8.