# Xam Idea Class 10 Maths Chapter 3 Solutions: Pair Of Linear Equations In Two Variables

Xam Idea Class 10 Maths Solutions for Chapter 3 ‘Linear equations In Two Variables’ are based on the latest guidelines prescribed by CBSE and NCERT. All the Xam Idea Solutions will help you to practice the concepts in a better and effective way. In this chapter, you will learn how to write linear equations in two variables, the graphical representation of the equations and how to find the solutions of linear equations. Our step by step solutions for the chapter will make the board exam preparations easy and organised.

Xam Idea Solutions for Class 10 Chapter 3 Linear Equations In Two variables contains 6 exercises in all. All the exercises include a mixture of questions including HOTS (high order thinking skill questions) and value-based questions that are important from the Class 10 board exam perspective. All these questions carry a heavy weightage in the question paper. You need to find the solutions of linear equations and then plot them on the graph. The exercises also include the equality concept of linear equations. All the questions are designed as per the latest guidelines of CBSE and NCERT.

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## Important Topics In The Xam Idea Class 10 Maths Solutions Chapter 3: Linear Equations In Two variables

The chapter includes the different ways of finding solutions of linear equations in two variables and gives you more clarity about the representation of linear equations. It also covers how to plot the Linear equations on the graph. Graphical method and the algebraic method of solving linear equations are also present in the chapter.

**Introduction And Graphical Methods**

- A linear equation in two variables is of the form ax+ by+ c =0 where a, b and c are real numbers and a, b is not equal to zero.
- The general form for pairs of linear equations in two variables is ax1 + by1 +c1 = 0 and ax2 + by2 + c2= 0 and all are real numbers.
- Each solution of a linear equation in two variables, ax + by + c= 0, corresponds to a point on the line representing the equation and vice versa.
- A pair of linear equations which has no solution is called an inconsistent pair of linear equations and in this case, the lines are parallel.
- A pair of linear equations in two variables which has a solution is called a consistent pair and in this case, the lines may intersect at a single point.
- A pair of linear equations which has equivalent and infinitely many solutions is called a consistent or dependent pair of linear equations and in this case, the lines coincide with each other.

**Algebraic Methods to Solve a Linear Equation in Two Variables**

**Substitution Method-**in this we have to find a value of any variable in any one equation and then have to substitute in other to find the answer.**Elimination Method-**In this we have to eliminate any 1 variable by making it equal in both the equations.**Cross Multiplication Method-**In this we follow a particular pattern to find the solution of the pair of equations.**Graphical Method-**In this we find the solutions of the pair of equations by plotting them on the graph and observing their structures.

### Exercise Discussion of Xam Idea Class 10 Maths Solutions Chapter 3: Linear Equations in Two Variables

**Very Short Answer Type Questions**

In this very short answer type questions, we have to answer in one or two words. There are total 20 questions in this exercise set, you will be given a pair of the equation and you have to find the values of x and y or you have to tell whether the pair of the equation is consistent or inconsistent

**Short Answer Type Questions-l**

This set includes 15 questions in total where you have to compare the constant terms and tell whether they are consistent or inconsistent. In this section, you also have to tell the situations of line on a graph that is if they are parallel or intersecting etc.

**Short answers Type Questions-ll**

There are a total of 12 questions in this set of exercise where you have to plot the equations on a graph. You also have to find the solutions of equations with any one method.

**Long Answer Type Questions****
**This section contains 10 questions in all where you have to read the statement and then form the equation. In addition, you have to find the solutions to the equations and then plot them on the graph. It also has a question in which you have to compare the values of constants and then find the answers.

**High Order Thinking Skills Questions**

This section contains 5 questions which are tricky and interesting as well. In this, you will have a confusing statement and you have to form the equations from the statement. It also Includes some graph questions such as you have to find value through a graph.

**Value-Based Questions**

In this section, you have 5 questions where you have to answer the statements and form the equations by including some basic value from life.

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