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Algebra 2 practice

Two-Equation Word Problem Worksheets

Build and solve systems of two equations from printable stories, with variable-definition lines and worked contextual answers.

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Define x and y, write two equations, solve the system, and state an answer with appropriate units.

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Model before solving

Define the two unknown roles, translate two independent facts into equations, and solve the resulting system.

Learning objective

What this activity builds

Translate two related facts into two equations and interpret the solution in context.

Worked example

Adult tickets cost $8 and child tickets cost $5. A total of 20 tickets brings in $130. How many of each were sold?

10 adult tickets and 10 child tickets.

Let x be adult tickets and y be child tickets. Then x + y = 20 and 8x + 5y = 130. Subtract five times the first equation to obtain 3x = 30.

Teaching notes

Make the practice count

  • Name both unknowns before writing equations.
  • Match each coefficient to its quantity and units.
  • Check the solution against both facts in the story.

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Four story cards ask students to define variables, build two equations, solve, and answer in context.

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Math SheetNameScoreTeacherDateTwo-Equation Word ProblemsDefine x and y, write a system of two equations, solve it, and answer in context.1.A jar holds 45 nickels and dimes worth 345 cents. How many nickels anddimes are in the jar?x =y =Equation 1:Equation 2:Solve:Answer in context:2.A school sold 62 concert tickets. Adult tickets cost $16 and student ticketscost $13. Ticket sales totaled $911. How many of each ticket were sold?x =y =Equation 1:Equation 2:Solve:Answer in context:3.At a school store, 2 notebooks and 1 pen cost $13. A second purchase of 1notebook and 3 pens costs $19. Find each unit price.x =y =Equation 1:Equation 2:Solve:Answer in context:4.A farm pen contains 32 chickens and rabbits. Together they have 86 legs.How many chickens and rabbits are in the pen?x =y =Equation 1:Equation 2:Solve:Answer in context:Define both variables before writing the two equations.math-sheet.comPage 1 of 1

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