TOP 30 Questions 🔥 |PAIR OF LINEAR EQUATIONS IN TWO VARIABLES| Class 10th BOARDS 2026⚡ | Aman Verma

Master Class 10th Maths Chapter 3: Pair of Linear Equations in Two Variables. Whether you are struggling with complex Word Problems or confused between Elimination and Substitution methods, this video provides a step-by-step roadmap to score full marks in your Class 10 Boards. [Key Concepts Breakdown] In this session, we cover the core pillars of Linear Equations: • Graphical Method: Understanding Intersecting, Parallel, and Coincident lines. • Consistency: How to tell if a system has a Unique Solution, No Solution, or Infinitely Many Solutions using coefficients. • Algebraic Methods: 1. Substitution Method (The 'replace' technique) 2. Elimination Method (The 'cutting' technique - most popular!) • Word Problems: Age-related, Speed-Distance, and Fraction-based problems solved with easy tricks. [Why This Video is a Must-Watch] If you have searched for any of these, you are in the right place: ✅ Linear Equations Class 10 One Shot Revision ✅ How to solve Linear Equations Class 10 Fast ✅ Elimination Method Class 10 Maths Chapter 3 ✅ Substitution Method Class 10 Important Questions ✅ Word Problems of Linear Equations Class 10 CBSE ✅ Pair of Linear Equations Class 10 Telegram: https://t.me/AVInevitableSuccess Time Stamps: 00:00 Intro 01:04 Q.1 If the pair of equations 2𝑥 + 3𝑦 = 7 and 4𝑥 + 𝑘𝑦 = 14 has infinitely many solutions, then the value of 𝑘 is: 07:51 Q.2 The pair of equations 𝑥 + 2𝑦 − 4 = 0 and 2𝑥 + 4𝑦 − 12 = 0 has: 11:08 Q.3 The pair of linear equations 𝑦 = 0 and 𝑦 = −5 has: 13:18 Q.4 For what value of 𝑘 is the system of equations 𝑥 + 2𝑦 = 5 and 3𝑥 + 𝑘𝑦 = 15 consistent? 19:05 Q.5 The graph of 𝑥 = −2 is a line parallel to the: 20:27 Q.6 If the lines 2𝑥 + 𝑦 − 3 = 0 and 4𝑥 + 2𝑦 − 6 = 0 are drawn, the number of intersection points are 22:51 Q.7 The value of 𝑚 for which the pair of linear equations 4𝑥 − 5𝑦 = 12 and 𝑚𝑥 + 15𝑦 = 36 has no solution is: 25:07 Q.8 Assertion (A): The equation 3𝑥 − 𝑦 = 8 has a unique solution. Reason (R): A single linear equation in two variables always has infinitely many solution. 27:14 Q.9 Solve the following pair of equations by Substitution Method: 𝑥 + 2𝑦 = 10 and 2𝑥 − 𝑦 = 5. 31:12 Q.10 Solve for 𝑥 and 𝑦 using the Elimination Method: 10𝑥 + 3𝑦 = 75 and 6𝑥 − 5𝑦 = 11. 35:58 Q.11 Find the value of 𝑘 for which the pair of equations 3𝑥 − 2𝑦 = 8 and 4𝑥 + 𝑘𝑦 = 20 has a unique solution. 40:49 Q:12 Solve for 𝑥 and 𝑦: 𝑥 / 2 + 𝑦 = 0.8 and 𝑥 / 7 + 𝑦 / 2 = 0.3. 46:23 Q.13 Determine whether the following system is consistent or inconsistent: 𝑥 − 2𝑦 = 0 and 3𝑥 + 4𝑦 = 20. 49:55 Q.14 Find the coordinates of the point where the line 𝑥 − 𝑦 = 5 intersects the 𝑥 − 𝑎𝑥𝑖𝑠. 53:53 Q.15 Solve for 𝑥 and 𝑦: 𝑥 / 𝑎 + 𝑦 / 𝑏 = 2 and 𝑎𝑥 − 𝑏𝑦 = 𝑎² − 𝑏² 01:00:30 Q.16 For what value of 𝑘 will the following system of equations have no solution? 3𝑥 + 𝑦 = 1 and (2𝑘 − 1)𝑥 + (𝑘 − 1)𝑦 = 2𝑘 + 1. 01:03:31 Q.17 Find the value of 𝑚 for which the pair of linear equations 2𝑥 + 3𝑦 − 7 = 0 and (𝑚 − 1)𝑥 + (𝑚 + 1)𝑦 = 3𝑚 − 1 has infinitely many solutions. 01:08:16 Q.18 Solve: 7𝑥 − 15𝑦 = 2 and 𝑥 + 2𝑦 = 3. Hence find the value of ‘𝑎’ for which 𝑦 = 𝑎𝑥 + 3. 01:15:04 Q.19 Determine graphically whether the pair of linear equations 3𝑥 − 𝑦 = 3 and 2𝑥 − 3𝑦 = 2 is consistent or inconsistence. 01:25:01 Q.20 Solve for 𝑥 and 𝑦: 𝑎𝑥 + 𝑏𝑦 = 𝑐 and 𝑏𝑥 + 𝑎𝑦 = 1 + 𝑐. 01:35:31 Q.21 Find the coordinates of the vertices of the triangle formed by the lines 𝑦 = 𝑥, 𝑦 = 0, and 𝑥 + 𝑦 = 4. 01:41:31 Q.22 Solve for 𝑥 and 𝑦: 47𝑥 + 31𝑦 = 63 and 31𝑥 + 47𝑦 = 15. 01:47:19 Q.23 The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction. 01:51:03 Q.24 Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu? 01:58:52 Q.25 The sum of the digits of a two – digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number. 02:08:05 Q.26 A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and the boat in still water. 02:21:29 Q.27 A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. A student A takes food for 20 days and pays ₹1000 as hostel charges. Student B takes food for 26 days and pays ₹1180. Find the fixed charges and the cost of food per day. 02:27:53 Q.28 Case Study 01 02:34:10 Q.29 Case Study 02 02:41:50 Q.30 Case Study 03 #MathsByAmanVerma #Class10Maths #LinearEquations #Chapter3Maths #CBSE2026 #MathsOneShot #SubstitutionMethod #EliminationMethod #ImportantQuestions #MathsTricks