Real World Example of Linear Equation

[billyb]

I'm a little stuck on this problem.

What is a real world example of a linear equation with infinitely many solutions?

 

[HallsofIvy]

I'm a little stuck on this problem.

What is a real world example of a linear equation with infinitely many solutions?

Do you mean a single equation or a system of linear equations?

 

[billyb]

System of linear equations

 

[Math is my friend]

System of equations with infinitely many solutions

2x + y = 3 and 4x + 2y = 6
OR
y = 3 - 2x and 2y = 6 - 4x

Do you know why?

 

[HallsofIvy]

Back around 1990, the United States government started a program to "reconcile" township lines in geodesic maps. If you, for example, look on 'old' maps you will see that the lines denoting townships don't always come together where they should- due to slight errors in the surveys of the individual townships. You could, of course, just shift one of the townships to match the other, but that would increase the error with the next one. Instead you need to set up equations matching each township with all 8 townships next to it. I don't recall all of the numbers but it involved something like 250000 simultaneous equations with about 200000 unknown values.

There is a non-technical discussion of that or a similar computation here: http://www.cadastral.com/gmm96ah.htm.