Final answer:
A treaty involves the system of checks and balances by requiring a two-thirds majority vote in the Senate, while an executive agreement usually bypasses the legislative branch.
Step-by-step explanation:
In the context of the U.S. system of checks and balances, treaties require a two-thirds majority vote in the Senate for approval, which reflects the involvement of the legislative branch in the treaty process. This process starts with the president negotiating a treaty, followed by the Senate providing its 'advice and consent' through the required vote, and concluding with the president ratifying the treaty. On the other hand, an executive agreement is generally entered into solely by the executive branch, often without the need for congressional approval, unless it involves commitments that may require legislative action, such as financial commitments. Therefore, the answer that demonstrates the system of checks and balances at work is: 'A treaty requires approval of the Senate with a two-thirds majority vote.'