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RD Sharma Class 9 Solutions Chapter 13 - Linear Equation In Two Variables (Ex 13.4) Exercise 13.4

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RD Sharma Class 9 Solutions Chapter 13 - Linear Equation In Two Variables (Ex 13.4) Exercise 13.4 - Free PDF

Free PDF download of RD Sharma Class 9 Solutions Chapter 13 - Linear Equation In Two Variables Exercise 13.4 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 13 - Linear Equation In Two Variables Ex 13.4 Questions with Solutions for RD Sharma Class 9 Maths are available to help you to revise the complete Syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. You can also register Online for Class 9 Science tuition on Vedantu.com to score more marks in your examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students.

Competitive Exams after 12th Science

Linear Equation in Two Variables

The system of equations called the linear equations in two variables have either a unique solution, no solution or infinitely many solutions. A system of linear equations may have a ‘n’ number of variables. While solving the linear equations with n number of variables, there must be n equations to determine and solve for the values of variables. The set of solutions that are obtained on the solution of these linear equations is a straight line and linear equations in two variables are the algebraic equations which are of the form y = mx + y where m is the slope and y is the y-intercept of the coordinates. As we can see, these are equations of the first order. 


What are Linear Equations in Two Variables?

As said earlier, the linear equations in two variables are of the highest exponent order of 1 and have a single, more or infinitely many solutions for them. ax + by + c = 0 is the standard form of a linear equation of two variables where x and y are the two variables. Solutions of linear equations with two variables can be written in ordered pairs. On representing the linear equations in two variables on a graph, we can observe two straight lines which could be two straight lines, two intersecting lines, parallel lines or coincident lines depending on the solution we obtain on solving them. 


Different ways of solving Linear Equations in two Variables

There are a total of five methods for solving linear equations in two variables:

 They are as follows. 

  • Graphical Method

  • Substitution Method

  • Cross Multiplication Method

  • Elimination Method

  • Determinant Method

 

How is linear inequality in two variables and linear equation in two variables similar to each other?

A linear inequality in two variables and linear equation in two variables are similar to each other in the following way:

  • The degree of a linear equation in two variables and linear inequality in two variables is always 1.

  •  Both linear equations in two variables and linear inequality in two variables can be solved using a graph.

  • The way to solve a linear inequality is somewhat similar to linear equations except that it is just separated by an inequality symbol.

FAQs on RD Sharma Class 9 Solutions Chapter 13 - Linear Equation In Two Variables (Ex 13.4) Exercise 13.4

1. How does one solve a linear equation in two variables? 

One can solve a linear equation in two variables using the following methods:

  • Graphical Method

  • Substitution Method

  • Cross Multiplication Method

  • Elimination Method

  • Determinant Method

2. How to solve linear equations in two variables using the graphical method?

The steps for solving a linear equation in two variables by the graphical method are given below.

  • Step 1: To solve a system of linear equations in two variables graphically, we represent each of the equations in a graph.

  • Step 2: To represent a  graph of an equation manually, first convert it to the form of y=mx+b by solving the given equation for y.

  • Step 3: Start substituting the values of x as 0, 1, 2, 3, and so on to find the corresponding values of y, or the vice-versa can also be done.

  • Step 4: Find out the point where two lines meet.

  • Step 5: The point of intersection of both the lines is the solution of the given system of linear equations in two variables. 

But, in some cases, both lines may not always intersect. Sometimes they may be parallel to each other. Thus, there will be no solution for  the system of linear equations in two variables in such a case. In some of the other cases, both lines coincide with each other. In those cases, each point on that particular line is a solution of the given system and hence, the given system has an infinitely number of solutions. If there is a solution for the system then it is called a consistent system; otherwise, it is said to be an inconsistent system.

3. How to solve linear equations in two variables using the substitution method?

The steps for solving a linear equation in two variables by the substitution method are given below.

  • Step 1: First, solve one of the given equations for one variable.

  • Step 2: Then, substitute this found variable into the other equation to get an equation in terms of a single variable.

  • Step 3: Solve it for the next variable.

  • Step 4: Then, substitute it in any of the equations to get the required value of another variable.

4. How to solve linear equations in two variables using the elimination method?

The steps for solving a linear equation in two variables by the elimination method are given below.

  • Step 1: Arrange the given equations in the standard form that is ax+by+c=0 or ax+by=c.

  • Step 2: Check all possibilities if adding or subtracting the equations would result in the cancellation of a variable anywhere.

  • Step 3: If it is not like this then multiply one or both the equations by either the coefficient of x or coefficient of y, such that their addition or subtraction would result in the cancellation of any one of the variables present.

  • Step 4: Solve the resulting equation with a single variable.

  • Step 5: Put it in any of the given equations to get the value of another variable from it.

5. How to represent linear equations in two variables graphically?

One can represent linear equations in two variables graphically using the following steps:

  • Step 1: A system of linear equations in two variables can be represented graphically by graphing each equation by converting it to the form y=mx+b by solving the equation for the y variable.

  • Step 2: Identify the points at which both the lines intersect.

  • Step 3: The point of intersection(s)  is/are the solution(s) of the given system of the linear equations in two variables.