Solving simultaneous equations graphically and algebraically to find a break-even point

What this note covers

1. Two relationships, one moment where they agree
2. Building the equations from a worded context
3. The graphical method: table of values, plot, read the intersection
4. The algebraic methods: substitution and elimination
5. Interpreting the answer: profit, loss and the meaning of the crossing point
6. Comparing two plans: the same mathematics without a break-even point
7. Working with whole items: floor and ceiling in break-even answers
8. How break-even questions are marked, and what lifts an answer to the top band

8 sections · 12 key terms & formulas · 6 common mistakes