12. Choosing a Method and Checking Reasonableness

Choose the method that matches the structure.

Use graphing when the intersection is easy to read and exact enough. Use substitution when a variable is already isolated. Use elimination when coefficients are lined up or can be made opposites.

A final answer should pass three checks:

1. It works in both equations.
2. It answers the question being asked.
3. It makes sense in context.

For example, a system about tickets should not produce a negative number of tickets. A break-even month should not be reported as a cost unless the question asks for total cost.

If a solution is \((4,2)\), read it in context. It might mean 4 adult tickets and 2 child tickets, or 4 months and 2 dollars, depending on variable definitions.

Common misconception: solving correctly but answering the wrong quantity. The pair is useful only when interpreted with labels.

Academic habit: write a short sentence after the ordered pair: "This means ..." That final sentence catches many GED® word-problem mistakes.