# RS Aggarwal Class 10 Chapter 3 Solutions (Linear Equations In Two Variables)

RS Aggarwal Solutions for Class 10 Chapter 3 are prepared to help you understand the graphical representation of linear equations. In this chapter of RS Aggarwal Class 10 Maths Solutions, you will solve simultaneous linear equations in two variables and then plot a graph for those equations. You will learn about algebraic methods of cross multiplication, elimination and substitution for solving the equations. You will identify consistent systems of equations and show how the system of equations have unique solutions.

RS Aggarwal Class 10 Maths Chapter 3 has 6 exercises consisting of 197 long and short questions. Also, there is a miscellaneous exercise of 27 multiple questions. The exercises of the chapter also include various word-problems based on the applications of the system of linear equations. The exercises of the chapter also include questions on consistent and inconsistent linear equations and their solutions. In some questions, you have to find the area of the polygon made by the graph of these equations.

Instasolv will help you reach the peak level of understanding of the chapter with easy and hassle-free RS Aggarwal solutions. With the help of these solutions, you can easily prepare for Class 10 board exams and score good marks. All the solutions are easy to understand and follow.

## Important Topics for RS Aggarwal Solutions for Class 10 Chapter 3: Linear Equation in Two Variables

**System of Linear Equations in Two Variables **

- You must have seen equations like 2x+5y=10 or x-y=5 very often. These are linear equations in two variables.
- Each of these equations has two variables x and y.
- So we can generalize a linear equation in two variables in the form of
**ax+by+c=0.** - Here a,b and c are constants and x and y are variables.
- ‘a’ is a coefficient of x and ‘b’ is a coefficient of y.
- Linear equations in two variables have two conditions:
- a,b and c are real numbers
- a
_{2}+b_{2}≠ 0

**Finding the Area of Triangle**

- A triangle can be found when values of linear equations are plotted on the graph. With the help of that graph, we can find the area of a triangle by its formula.
- The formula of area of the triangle is ½ * base * height

**Algebraic Methods of solving A Pair of Linear Equations**

In algebraic methods, there is no need for graph and point plotting. If the equations have non-integral coordinates, it is not possible to solve them graphically. Therefore, algebraic methods are alternatives to solve linear equations in two variables.

**Substitution Method**

An equation can be solved by this method when you find one variable from either equation and substitute its value in the other equation.

For instance, x+2y=3 and 4x+5y=6

Step 1: Let’s consider equation (1), x+2y=3

So we write as x=3-2y

Step 2: Substituting the value of x in equation (2), 4x+5y=6

We have 4(3-2y)+5y=6

12-8y+5y=6

12-3y=6

y=2

Step 3: Substituting the value of y in x=3-2y, we have x= 1

Final answer: x=1, y=2

**Elimination Method**

This method is considered more convenient. It is solved by multiplying both the equations by some non zero constant and after that adding or subtracting one equation from another to eliminate one variable. By solving one variable you obtain the value of another variable by substitution.

**Cross-Multiplication Method**

This method is followed by cross multiplication technique. Suppose we have two linear equations:

Equation 1: a_{1}x + b_{1}y + c_{1} = 0

Equation 2: a_{2}x + b_{2}y + c_{2} = 0

The values of x and y are given by:

**Equation having a Unique Solution**

- Suppose we are considering two linear equations:

Equation 1: a_{1}x + b_{1}y + c_{1} = 0

Equation 2: a_{2}x + b_{2}y + c_{2} = 0

- A system of equations is said to be having unique solutions when a
_{1}/a_{2}≠ b_{1}/b_{2} - Let say for an example 1x +2y= 3 and 4x+5y=6,
- So, for a given equation, a
_{1}=1, b_{1}=2 and a_{2}=4, b_{2}=5 and c_{1}=3, c_{2}=6 - Here, a
_{1}/a_{2}≠ b_{1}/b_{2}so, the system has unique solutions.

**Equation having an Infinite Solution **

A system of equations is said to be having infinite solutions when a_{1}/a_{2} = b_{1}/b_{2}

**Equation having No Solution**

When a system of equations has a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}, the equations are said to be having no solution.

### Exercise Discussions for RS Aggarwal Solutions for Class 10 Chapter 3: Linear Equation in Two Variables

- In exercise 3A, you are asked to solve the basic linear equations and find the coordinates. For that, it is necessary to find the area of a triangle by solving equations graphically.
- In exercise 3B, you will encounter equations that will be solved using the elimination method and the substitution method.
- In exercise 3C, you have to apply cross-multiplication to get to solve the linear equations. In some questions, you might require to apply some assumptions so as to form the standard linear equations.
- Exercise 3D is full of word problems in which it is often asked to find the value of
*k*. Few questions ask you to solve the equations by cross-multiplication method. - In exercise 3E, questions regarding finding the numbers of solutions of the linear equations. In some questions, you are already given what kind of solutions the system of linear equations has and you have to find the solutions. You are also asked to plot the trapezium on a graph and find the coordinate of the vertices.
- In Exercise 3F, you will have to identify if the system of equations has a unique solution or no solution or infinite solution.

### Benefits of RS Aggarwal Solutions for Class 10 Chapter 3: Linear Equation in Two Variables

- Instasolv has solved each question in a detailed manner with a brief explanation.
- As this chapter is not easy to understand, Instasolv has managed to explain every formula and assumptions with reason. This will enable you to understand the process of solving a linear equation.
- Graphical questions need to be understood thoroughly to solve it correctly. Therefore, we provide a complete and clear solution to guide you with all the difficulties.
- The exercises comprise various word problems. Instasolv will provide you with the best and easiest solutions of all.
- Learning this whole huge chapter is a challenge. Hence, we make sure that no problem is skipped in the RS Aggarwal Solutions for Class 10 Chapter 3.
- With each question, Instasolv assures its authenticity and clarity.