SAT Math: Setting Up Systems of Equations from Word Problems
41+ practice questions in Praczo
The concept, explained
- 1
Use a system when a problem has two unknown quantities and two distinct relationships. Define both variables explicitly before writing any equation.
- 2
Write one equation per constraint. One usually involves a total (sum), the other involves a different relationship (cost, difference, ratio, rate).
- 3
Label each equation by what it represents — "total items" vs. "total cost" — to stay organized under test pressure.
- 4
After solving, re-read the question. It may ask for x + y, or just one variable, not necessarily whatever you solved for first.
- 5
Substitution is cleanest when one equation is already solved for a variable. Elimination is faster when both are in Ax + By = C form.
- ✗ Writing two equations that express the same constraint differently — double-check that both equations reflect genuinely different relationships.
- ✗ Solving for x when the question asks for y, or for one variable when it asks for their sum.
SAT-style practice
Adult tickets to a play cost (12 and student tickets cost )7. A group purchased 20 tickets total and paid $185. How many student tickets were purchased?
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