What are real-life examples where a linear equation would end up being a Contradiction or Identity? In Algebra, linear equations in one variable can have either one solution (i.e. $x=3$), infinitely many solutions (i.e. $2x+6=3(x+2)-x$ ), or no solution (i.e. $x+3=x+5$).
What would be some real-life situations where an equation would end up being a contradiction or identity and that would reveal something about what the equation represents?
 A: Suppose you have two objects you are tracking in deep space, and you would like to know if they will collide or not. You could wait a while and see what happens, or maybe you can kind of look at where they're going and guess at what will happen. Neither of these answers seems very satisfactory (or very mathematical). A better solution might be that if you know the positions in space, and the direction and speed the objects are moving in, you could construct a system of equations containing the position equations of each of these objects. If there is a single solution, the objects will collide, because the solution to the equation will be the point where the two objects have the same location. If there is no solution, the two objects will never occupy the same location at the same time. And if there are infinitely many solutions, then your two objects are always at the same location. This is just a very simple application of linear algebra, there are many more, and much more clever, ways of using linear algebra to solve real world problems.
