Class 10 Maths Most Important Questions Ch 3 Linear Equations in Two Variables

Linear equations in two variables are a fundamental concept in mathematics, particularly in Class 10. This topic appears frequently in board exams. To help students master this topic, it is very important to practice a variety of problems and understand the key concepts thoroughly.

Here, we will discuss the most important questions related to linear equations in two variables for Class 10. We'll also include extra practice problems that will help in revising the concepts. These are the premium questions directly from our book. 

‍

PREMIUM EDUCART QUESTIONS

<cta2> Download <cta2>

(Most Important Questions of this Chapter from our 📕)

‍

In the table given below, we have provided the links to Linear Equations In Two Variables Class 10 Important Questions downloadable PDFs. Now you can download them without requiring you to login.

What are Linear Equations and why are They Important? 

A linear equation in two variables takes the general form:

ax+by+c=0

Here:

• x and y are the variables.
• a, b, and c are constants (with a and b not both being zero).

This equation represents a straight line on the Cartesian plane. Every point on this line is a solution to the equation.

Why Is It Important?

Understanding linear equations in two variables is important because:

• These equations solve a wide range of real-world situations such as budgeting, predicting profits, and calculating distance. 
• Understanding this concept prepares students for more complex topics such as algebra and calculus.
• Linear Equations in two variables frequently appear in board exams, and being able to solve them quickly and accurately is important for scoring well. 

Linear Equations Class 10 Important Questions

The following are some of the most linear equations in two variables Class 10 important questions that you should focus on. These questions are designed to test a variety of skills, from basic solving techniques to understanding more complex scenarios.

Question 1: Very short answer type questions

This may include MCQs, Assertion/reason, and fill-in-the-blanks

Example: The value of a so that the point (3, a) lies on the line represented by 2x – 3y = 5, is .......

Question 2: Short Answer type questions

Find the value(s) of k for which the pair of equations kx + 2y = 3 and 3x + 6y = 10 has a unique solution.

Question 3: SA II 

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr; it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Question 4: Long Answer type question

A shopkeeper sells a saree at a profit of 8% and a sweater at a discount of 10%, thereby getting a sum ₹1,008. If she had sold the saree at a profit of 10% and the sweater at a discount of 8%, she would have got ₹1,028. Find the cost of the saree and the list price (price before discount) of the sweater

Question 5: Consistency of Equations

Check whether the following system of equations has a unique solution, no solution, or infinitely many solutions:2x+3y=7 4x+6y=14x

This problem focuses on understanding the concept of consistency in linear equations.

Tips for Solving Linear Equations in Two Variables

Acing the topic of linear equations in two variables requires practice and a good understanding of different solving techniques. Here are some tips to help you:

• Carefully read the question to identify what is being asked and what the variables represent.
• Depending on the nature of the problem, choose the most efficient method (substitution, elimination, or graphical) to solve the equations.
• Always substitute your solutions back into the original equations to verify that they satisfy both equations.
• Being able to accurately plot equations on a graph can help you visualize the solution and understand the relationship between the variables.
• Practice converting word problems into algebraic equations. This skill is essential for solving real-life problems using linear equations.

Linear equations in two variables is a topic that plays a vital role in the Class 10 mathematics syllabus. The ability to solve these equations and understand their applications is not only essential for exams but also for everyday problem-solving. By practising the linear equations class 10 questions and the extra questions provided here, students can strengthen their grasp of the topic and enhance their mathematical skills.