The material should indicate that systems of equations before and after their transformation by the multiplicative property are equivalent systems. Even the low level of difficulty should include cases requiring both methods of elimination. Moderate difficulty should involve fairly complex equations including fractions. Especially valuable are cases with variables in the denominator, and the method for solving these systems should be clarified. The highest level should include finding solutions in terms of other variables included in the equations.
Proof is desired.
Problem solving with systems of equations This subtopic will sometimes appear as a separate section. In other cases, it may be mixed into other subtopic areas and have to be evaluated by considering each of these. Too often this is not reinforced. Assigning the variables - The habit of explicit statements of what the variables stand for should be encouraged, and this should be done in more complex cases. In more complex cases, the meanings of the equations should be expressed.