--- title: "Equations with Two Unknowns" description: "Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15)" canonical: https://lightmysky.com/learn/mathematics/equations-with-two-unknowns-mt_YFS7JFk64p source: https://lightmysky.com/learn/mathematics/equations-with-two-unknowns-mt_YFS7JFk64p.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Equations with Two Unknowns Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15) Subject: Mathematics · Area: Algebra · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/equations-with-two-unknowns-mt_YFS7JFk64p ## Ready when they can - List all whole-number pairs (a, b) where a + b = 12 with a, b > 0 - Find three pairs that satisfy 2x + y = 20 - Explain systematically how to generate all integer solutions to a two-variable equation within a given range ## Lesson: Equations with two unknowns You know how to write an equation like a + b = 10. Now think about solving it. This equation does not have just one answer. It has many. Any pair of numbers that adds up to 10 makes the equation true. *(drawing: Here, a = 4 and b = 6. Check it: 4 + 6 = 10, so this pair fits the rule.)* **Example.** Mia wants a pair of numbers for 2x + y = 20. She picks x = 5. Two times 5 is 10, so y must be 10 to make the total 20. The pair (5, 10) works. **Tip.** To find more pairs, pick a number for one unknown, then work out what the other one has to be. Change your first pick and you get a new pair every time. **Recap.** Many pairs of numbers can make the same equation true. Pick one unknown, solve for the other, and you have found a pair. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Writing Algebraic Equations](https://lightmysky.com/learn/mathematics/writing-algebraic-equations-mt_i9rJbuFO3p) ## Opens up - [Simultaneous equations](https://lightmysky.com/learn/mathematics/simultaneous-equations-mt_mqgu72aCMz)