When+are+there+infinitely+many+solutions+(and+how+do+we+specify+exactly+which+solutions+we+mean)?Set+6

Give an example of a system of equations that has infinitely many solutions. Ask your classmate to demonstrate at what point in the solving (substitution or elimination) it is indicated that there are infinitely many ordered pairs that satisfy both equations. Also insist that your classmate not just say that the solution is "all real numbers" because in fact we are looking for ordered pairs that satisfy the equation -- so how do which specify which of the infinitely many ordered pairs that are available to us in the universe we want? Just because there is more than one doesn't mean that we can use every possibility!!