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

## 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.