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There are several ways to eliminate a value in an array that corresponds to a value in a different array, depending on the programming language and specific requirements. Here is a general process using pseudocode:

1. Define the two arrays and the value to be eliminated from the first array.

array1 = [1, 2, 3, 4, 5]
array2 = [2, 5, 7, 9, 10]
value_to_remove = 2

1. Find the index of the value to be removed in the first array using a loop or a built-in function.

index_to_remove = -1
for i from 0 to length of array1:
  if array1[i] == value_to_remove:
    index_to_remove = i
    break

1. Check if the value to be removed also exists in the second array, using a loop or a built-in function.

is_duplicate = false
for j from 0 to length of array2:
  if array2[j] == value_to_remove:
    is_duplicate = true
    break

1. If the value is a duplicate, remove it from both arrays using the same index.

if is_duplicate:
  array1.pop(index_to_remove)
  array2.pop(index_to_remove)

Note that this process assumes that both arrays have the same length and that there is only one instance of the value to be removed in the first array. If these assumptions do not hold, adjustments may be necessary.