Linear Equations in Two Variables: Definition, Methods

Linear Equations in Two Variables: It is an equation written in the form ax+by +c=0. a, b, and c are real values, whereas x and y are variables. We can say that a and b are not equal to zero. Linear equations are solved when the same number is added to both sides, as well as when both sides are multiplied and divided by the same amount. Linear equations with two variables are denoted by x and y.

This is the most significant topic for students in secondary school since it teaches them how to solve mathematical problems quickly. For a better understanding, see the NCERT Solutions for Class 9 Maths Chapter 4. This page contains in-depth information on linear equations with two variables. Read on to know about its definition and solve examples.

Linear Equations In Two Variables: Definition

Linear equations in two variables are also known as an equation that has two unknown variable quantity and its degree is two. It is expressed in the form of ax + by + c=0, where a, b and c are coefficients, x and y are the variables and a and b are not equal to zero. Here, the x and y are the solutions to the equation. We can say that the equation is consistent if there is one solution and equation is in-consistent if there are no solutions. For example, 3x + 2y = 8 is a linear equations in two variables.

Methods To Solve Linear Equations In Two Variables

There are different methods through which you can solve linear equations in two variables as mentioned below:

Graphically
Substitution method
Cross multiplication method
Method of Elimination
Determinants method

Linear Equations In Two Variables: Solved Examples

Example 1: Give the geometric representations of 2x + 9 = 0 as an equation in two variables

Solution:

Linear Equations in Two Variables: Definition, Methods

Example 2: The cost of a notebook is twice the cost of pen write a linear equation in two variables to represent this statement.

Solution: Let the cost of a notebook be ₹ x and cost of pen be ₹ y

Given that cost of a notebook = 2 × cost of a pen

⇒ x = 2y ⇒ x − 2y = 0

Hence, x − 2y = 0 is the representation of the given statement

FAQs On Linear Equations In Two Variables

The frequently asked questions on linear equations in two variables are given below:

Q. What is linear equations in two variables?
A. Linear equations in two variables are known as an equation that has two unknown variable quantity and its degree is two.

Q. How is linear equations in two variables expressed?
A. It is expressed in the form of ax + by + c=0, where a, b and c are coefficient, x and y are the variable and a and b are not equal to zero.

Q. What are the different methods used to solve linear equations in two variables?
A. The different methods used to solve linear equations in two variables are as follows:
1. Graphically
2. Substitution method
3. Cross multiplication method
4. Method of Elimination
5. Determinants method

Q. How many solutions are there for two-variable linear equations?
A. There are an endless number of solutions to linear equations in two variables.

Q. What exactly is a two-variable equation?
A. A linear equation in two variables is one that has two distinct solutions.

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