➕ Algebra 1 · Systems of Equations
Systems Word Problems cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The plan (SOLVED)
- S: Say what each variable means (units)
- O: One equation for each fact
- L: Look for the easiest method
- V: Values: solve for both
- E: Examine the answer in the story
- D: Deliver a sentence with units
Translate
- Count: (number of A) + (number of B) = total number
- Value: (price A)(number A) + (price B)(number B) = total value
- Plan: cost = fee + rate × amount
- Distance = rate × time
Which method?
- A variable is alone: substitution
- Standard form: elimination
- Want the picture: graph (confirm by substituting)
Special cases
- False leftover, like 15 = 9: never equal (no solution)
- True leftover, like 0 = 0: always equal (infinitely many)
- Answer not whole or negative for a count: not viable
Watch out
- Do not add tickets to dollars
- Do not round a nonviable answer
- Check the story, not just your equations
Formulas
- Count equation: (number of A) + (number of B) = total number
- Value equation: (price of A) × (number of A) + (price of B) × (number of B) = total value
- Plan cost: cost = fixed fee + (rate) × (amount)
- Distance: distance = rate × time
Systems Word Problems cheat sheet from HighSchoolQ.com, for personal study use.