Systems of equations word problems worksheets

A system of equations is easiest to see as a scene: two things you do not know, and two facts that pin them down. These free printable worksheets give that scene — two containers, or two shopping baskets — and ask a child to name both unknowns and solve.

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Systems of equations word problems

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What's on this sheet

Two shapes cover the standard cases. In the first, two like quantities have a given sum and difference — two jars holding so many marbles between them, one with a few more than the other — which sets up x + y and x − y. In the second, two goods are bought in two different baskets at fixed prices, so three apples and two pears cost one amount and a different mix costs another; the unit prices are the unknowns.

Why this sheet works

Every problem is built backward from whole-number answers, so a child never lands on 3.5 apples or half a marble — the arithmetic checks out cleanly and the focus stays on the setup. Each story names both unknowns and always says which quantity is larger, so a sum and a difference is never left as a puzzle about which container holds more.

How this one works

One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.

Systems of equations word problems, step by step

Word problemsSystems of equations

Name: Date:

Read each problem. Write the answer.

1The top shelf holds 9 more books than the bottom shelf, and the two together hold 65 books.How many books are on the top shelf, and how many on the bottom shelf?The top shelfThe bottom shelf

2One shopper buys 2 peaches and 1 apple for $8. Another buys 2 peaches and 3 apples for $16.What is the price of one peach and one apple?One peachOne apple

3The left drawer and the right drawer hold 46 crayons altogether, and the left drawer has 14 more than the right drawer.How many crayons are in each?The left drawerThe right drawer

4Together, 4 notebooks and 1 pen cost $22. On a second visit, 4 notebooks and 4 pens together cost $28.Find the price of one notebook and one pen.One notebookOne pen

Word problems · Systems of equationsAnswer key

1. (65 + 9) ÷ 2 = 37, then 65 − 37 = 28, so 37 and 28 books2. a = peach, b = apple: subtract to remove a → 2b = 8, so b = 4; then 2a + 1 × 4 = 8, so a = 2 — a peach costs $2 and an apple costs $43. (46 + 14) ÷ 2 = 30, then 46 − 30 = 16, so 30 and 16 crayons4. a = notebook, b = pen: subtract to remove a → 3b = 6, so b = 2; then 4a + 1 × 2 = 22, so a = 5 — a notebook costs $5 and a pen costs $2

Systems of equations word problems worksheets

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