Class 10 Maths — Chapter 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

What you'll learn

• ▸Forming a Pair of Linear Equations from Word Problems
• ▸Graphical Method of Solving Linear Equations
• ▸Graphical Interpretation of Solutions
• ▸Consistency and Inconsistency of Linear Equations
• ▸Conditions for Consistency using Coefficient Ratios
• ▸Algebraic Interpretation from Coefficient Ratios

Chapter Summary

--- PAGE 1 --- 1062CH03 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 3 3.1 Introduction You must have come across situations like the one given below : Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a ring on the items kept in a stall, and if the ring covers any object completely, you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs ₹ 3, and a game of Hoopla costs ₹ 4, how would you find out the number of rides she had and how many times she played Hoopla, provided she spent ₹ 20. May be you will try it by considering different cases. If she has one ride, is it possible? Is it possible to have two rides? And so on. Or you may use the knowledge of Class IX, to represent such situations as linear equations in two variables. Reprint 2025-26 --- PAGE 2 --- PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 25 Let us …

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Explain real-world linear equations simply. Get Solution →
2. Graph different types of line solutions. Get Solution →
3. Solve a puzzle using two variables. Get Solution →
4. According to the text, what is a pair of linear equations that has no solution called? Get Solution →
5. What is the graphical representation of a pair of linear equations that has a unique solution? Get Solution →
6. If two lines representing a pair of linear equations are coincident, how many solutions does the pair of equations have? Get Solution →
7. For a pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, what is the condition for the lines to be intersecting? Get Solution →
8. What is the condition for a pair of linear equations to represent parallel lines? Get Solution →

Did you know?

• 💡 The equals sign "=" was invented in 1557 to avoid writing "is equal to".
• 💡 Ancient Babylonians used early forms of linear equations over 4,000 years ago.
• 💡 René Descartes developed coordinate geometry while watching a fly on his ceiling.
• 💡 Linear equations are fundamental to modern computer graphics and animation.
• 💡 A single straight line visually represents an infinite set of solutions.

Frequently Asked Questions

Related Chapters