Pairs of Equations സമവാക്യജോടികൾ
A table and a chair cost ₹11000; a table and four chairs cost ₹14000. What does each cost? Puzzles like this have two unknowns, and this chapter shows how to catch both: first with clever mental arithmetic, then with algebra – two letters, two equations, and the trick of making one letter disappear. An interactive, animated self-study guide: the basics from earlier classes, every idea of the chapter with real-life examples, animated solutions to every textbook question, a revision sheet, and a model test with a fully solved paper.
How to use this guide
🎬 Watch the animations
Every method is a step-by-step animation. Press Next ▶ to move one step at a time, or ▶▶ Auto play to watch it like a video.
🖐️ Play with the numbers
Sliders change prices, totals and coefficients. Watching the extra cost point straight at the missing price is the fastest way to feel how elimination works.
✍️ Try before you see
Questions come with a Show a hint button and a hidden final answer. Always try in your notebook first – mentally, with one letter, or with two equations.
📖 Textbook links
Purple മലയാളം words are the exact terms used in your textbook, so you can match every page here with the book (pages 7–18).
Learning path
Follow the pages in order. If you are comfortable writing and solving one-letter equations, you may skim pages 1–4, but do try their quizzes.
The chapter in one picture
Basket 1 has 2 pens and 3 notebooks; basket 2 has 2 pens and 5 notebooks. The shop only tells you the two totals. The second basket has exactly 2 notebooks more, so the difference of the totals is the price of 2 notebooks – the pens have disappeared! That trick, done with letters, is called elimination, and it is the heart of this chapter.
Quick glossary (Malayalam ↔ English)
| Textbook term | English | Meaning |
|---|---|---|
| സമവാക്യം | Equation | A statement that two expressions are equal, e.g. 2x + 3 = 13 |
| സമവാക്യജോടി | Pair of equations | Two equations about the same two unknowns, solved together |
| ബീജഗണിതം | Algebra | Using letters for numbers and working with them |
| മനക്കണക്ക് | Mental arithmetic | Working it out in your head by reasoning |
| പരിഹാരം | Solution | The values of the letters that make every equation true |
| തുക / വ്യത്യാസം | Sum / difference | x + y / x − y |
| മടങ്ങ് | Times (multiple) | "5 മടങ്ങ്" = five times |
| അംശം / ഛേദം | Numerator / denominator | Top / bottom of a fraction |
| ലഘൂകരിക്കുക | Simplify | Write in a simpler form: 4/8 = ½ |
| ചുറ്റളവ് | Perimeter | 2 × (length + breadth) for a rectangle |
| പലിശ | Interest | Money earned on an investment, e.g. 7% a year |
| വേഗം | Speed | Distance per second; u + at when it grows steadily |
Made for self-learning. Works offline – every page is a single file. Study material prepared by Claude for Madhu's family study folder, October 2026.