Why this chapter matters
Systems answer comparison questions such as when two plans cost the same or which combination of quantities meets two constraints.
What you will learn
- Solve two-variable systems by three standard methods.
- Recognize systems with one, none, or infinitely many solutions.
- Translate a two-condition word problem into a system.
Lessons in this chapter
- Graphing systemsUse intersection points as shared solutions.
- SubstitutionReplace one variable with an equivalent expression.
- EliminationCombine equations to remove one variable.
- Systems in contextInterpret a solution with units and real constraints. Read the full guide →
Study task
Create a system for adult and student tickets when 120 tickets earn $1,020, then solve and verify the ticket counts.
Chapter checkpoint
Solve x + y = 9 and x - y = 3.
Add the equations to get 2x = 12, so x = 6. Substitute to get y = 3.