SAT Math · Module 2: Heart of Algebra
Linear systems word problems
About this lesson
Word problems are where the SAT hides its algebra. The math is usually a simple two-variable system — the hard part is translating sentences about concert tickets, rental cars, and aquarium tickets into equations you can actually solve.
In this lesson you'll build a repeatable four-step routine: name the variables, write one equation per sentence, solve by elimination, then check the answer against the question that was actually asked. The worksheet gives you eight graded problems to practice the routine before the module quiz.
- Translate rate, cost, and distance sentences into two-variable systems
- Choose elimination or substitution in under ten seconds
- Spot the trap answer that solves for the wrong variable
Lesson cheat sheet
The three moves from this lesson, kept open while you work the worksheet.
The four-step translation routine
1. Name the variables out loud ("let t be the ticket price"). 2. Write exactly one equation per sentence — never two ideas in one line. 3. Solve the system. 4. Re-read the question and answer what it asked, not what you solved for.
Elimination vs. substitution
Reach for elimination when both equations are in standard form (ax + by = c) — one multiplication usually lines the coefficients up. Reach for substitution when a variable is already isolated or has a coefficient of 1.
Rate × time = distance
For combined-work problems, add the rates, never the times. If Ana paints a room in 3 hours and Ben in 6, their rates are 1/3 and 1/6 of a room per hour — together 1/2, so 2 hours.
My notes
Pinned to the video timestamp, so future-you knows exactly where to jump.
- 04:12
Difference of squares keeps showing up — review factoring before the quiz.