Final answer:
None of the operations (addition, subtraction, multiplication, division) results in an expression equivalent to 3x + y when applied between (7x - 3y) and (x - y). Hence, there is no correct option among the provided choices for what belongs in the box to make the expressions equivalent.
Step-by-step explanation:
The expression given can be understood as combining two expressions to obtain 3x + y as a result. To determine what operation belongs in the box, we need to perform the operation with 7x - 3y and (x - y) respectively, to see which operation results in 3x + y. We can test the operations from the options provided: addition, subtraction, multiplication, and division.
Let's eliminate options one by one:
Let's try multiplying (7x - 3y) by (x - y):
7x * x = 7x^2
7x * (-y) = -7xy
-3y * x = -3yx
-3y * (-y) = 3y^2
The result of this multiplication will be a quadratic expression (7x^2 - 7xy - 3yx + 3y^2), which is also not equivalent to the linear expression 3x + y.
Thus, none of the provided operations can be placed in the box to make the expression equivalent to 3x + y.