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Worksheets›Algebra 1›Equations & inequalities›Systems of equations word problems

Systems of Equations Word Problems Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 1CCSS HSA.CED.A.3Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Sum and difference of two numbers

  1. 1.Two numbers add to 29, and their difference is 1. Find the two numbers.
  2. 2.Two numbers add to 62, and their difference is 24. Find the two numbers.
  3. 3.Two numbers add to 23, and their difference is 1. Find the two numbers.
  4. 4.Two numbers add to 15, and their difference is 11. Find the two numbers.
  5. 5.Two numbers add to 56, and their difference is 10. Find the two numbers.
  6. 6.Two numbers add to 57, and their difference is 37. Find the two numbers.
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Name the two unknowns, then write one equation for each fact in the story: usually one counts the items and the other adds up their values. Solve by substitution or elimination, and answer the question that was asked, with units.

EasyTwo numbers add to 55, and their difference is 41. Find the two numbers.Sum and difference of two numbersMediumA theater sold 144 tickets for $1436. Adult tickets cost $12 and child tickets cost $8. How many adult tickets were sold?TicketsHardA jar holds 29 quarters and dimes worth $4.40 in all. How many quarters are there?Coins

How to solve it: a worked example

Write a system of equations and solve it.

  1. StartTwo numbers add to 103, and their difference is 1. Find the two numbers.
  2. Write the systemx + y = 103, x − y = 1
  3. Add the equations2x = 104, x = 52
  4. Substitute backy = 103 − 52 = 51
  5. Answer52 and 51

Common mistakes to watch for

  • Writing both equations from the same fact.
  • Mixing up which price goes with which kind of item.
  • Answering with the other unknown than the one asked for.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Multi-step inequalitiesAbsolute value equationsLiteral equationsCompound inequalitiesDirect and inverse variation

FAQ

How do you set up a system from a word problem?

Name the two unknowns, then write one equation for each fact in the story, such as one for the number of tickets and one for the total cost.

Why do these problems need two equations?

Two unknowns need two independent facts to pin them down. One equation alone, like a + c = 20, has many solutions.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix systems of equations word problems with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.