I am in Salt Lake City, UT with thousands of other high school and college faculty grading AP US Government and Politics exams. For the unfamiliar, high school students who pass AP exams are generally (but not always) given college credit for the introductory level course in that field. So, the curriculum is very similar to what one teaches in Political Science 101 – American Government at the college level.
I've graded over 1000 responses, personally, to the same question about checks and balances. That's not a spoiler; the exam was taken a month ago and besides, how does any American Govt class at any level not prepare the students to answer a basic question about checks and balances, separation of powers, and so on. Since all I am doing, 8-9 hours per day, is reading responses to this single question, it has me thinking of how I like to cover this in the classroom.
Take maybe 30 feet of rope to class. Solicit three volunteers to sit or stand in a triangle and connect to one another by looping the rope around their waist (or through 2-3 belt loops) and then to the next person. Ask them to stand apart so that the rope has no slack.
Very quickly they realize that any single person moving is impossible. Perhaps they can stretch it a little bit, but only a little – provided the other two pull back.
Then try the same thing except have the volunteers form a triangle simply by holding on to the rope with one hand. Now when one person tries to move, he or she actually has a decent amount of leeway to move even if the other two remain stationary. Arms are long and they move in nearly any direction. But still, there is a limit. One person can walk away from the other two for a few steps, but then the rope runs out.
Eventually we return to the belt/waist example, where it was harder for any one person to walk away. And I ask, what is the only way the Executive Branch can get from this classroom to the classroom across the hall while tied to Mr. Legislature and Ms. Judiciary like this?
Since this isn't rocket science, someone chimes in pretty quickly with the only non-smartass answer: Executive Branch can move wherever he wants if the other two branches are willing to come with him. Alternatively, the cooperation of one other branch could make, say, Executive and Legislature strong enough to drag Judiciary where she doesn't want to go.
As long as two branches are trying to hold their ground, no matter what manner is used to tie the three together the range of possible motion will be limited. The area to which they are confined, and to which they drift back no matter how hard an individual tries to run away, is the Constitution. The rope is checks and balances. The point, then, is that checks and balances preserve the system defined by the Constitution only inasmuch as all three branches (or two of three) are unwilling to consent to walking away to a different classroom altogether.
The nation began with the rope-around-waist version because the people who came up with this conceived of political competition as among the branches of government ("Congress rules!" vs "Booo, President #1!"). Then political parties changed the way political actors identify from the institution to the coalition. So each branch has had a lot of room to walk around – the rope-in-hand version. We may be about to see the transition to the last example.