In previous classes, you have studied the linear equations in one variable. In class 9, linear equation in two variables, chapter 4, we are going the discuss how to solve the linear equations in two variables, linear equations solutions and graphs to represent the equation in detail. Here, you are provided with the notes to understand the concept in an easy way.

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## Linear Equations in Two Variables Class 9 Topics

The topics and subtopics covered in class 9 chapter 4 are given below:

- Introduction
- Linear Equation
- A solution of a Linear Equation
- Graph of a Linear Equation in Two Variables
- Equations of Lines Parallel to the x-axis and y-axis

## Linear Equation in Two Variables Class 9 Brief Notes

Here, the brief notes on chapter 4, linear equations in two variables class 9 are given here. Go through the below points to be clear with the concepts.

- A linear equation in two variables is an equation, which is of the form
**ax + by + c = 0,**Â Here, a, b and c are real numbers, such that a and b are non zero values - It has infinitely many solutions.
- When you draw a graph for every linear equation in two variables, it is always a straight line
- The equation of y-axis is x = 0 whereas the equation of the x-axis y = 0
- The graph of equation x = a is a straight line, which is parallel to the y-axis.
- The graph of equation y = a is a straight line, which is parallel to the x-axis.
- An equation y = mx is also a line equation, which represents a line passing through the origin
- It is noted that every point on the graph of a linear equation in two variables is a solution of the linear

equation. Moreover, every solution obtained for the linear equation should be a point on the graph of the

linear equation.

### What is Linear Equation in Two Variables?

Each linear equation in two variables can be defined in a straight line. To solve a system of two linear equations in two variables, we graph both equations in the same coordinate system. The equation that can be represented in the form of px + qy + r = 0 is called a two-variable linear equation. [where p, q & r are real, and p & q are not 0]. For example: 2.5p + 3q = 9, x + 8y = 9, 9u â€“ 15v = 19, etc..

### Linear Equations in Two Variables Solutions and Graphs

There are infinitely many solutions possible for a linear equation in 2 variables. The graph of such equations is always a straight line. In a two-variable linear equation, x = 0 denotes the equation of y-axis and y = 0 denotes the equation of the x-axis. The graph of equation x = c represents a straight line parallel to the y-axis.

Similarly, the graph of equation y = c represents a straight line parallel to the x-axis. The equation y = cx (where c = constant) represents a line passing through the centre (origin). All the points on the graph of a 2 variable linear equation is a solution of the linear equation. The graph of a linear equation represents the solution of a linear equation. The solution remains unaffected when:

- The same quantity is either subtracted or added from both the sides (LHS and RHS) of the equation.
- If both LHS and RHS of an equation are multiplied or divided by the same non-zero number.

### Linear Equations in Two Variables Class 9 Important Questions

Solve the practice the important questions given below.

**Q.1)** Write each of the following as an equation in two variables:

(i) y = 2 (ii) x = â€“5 (iii) 5y = 2 (iv) 2x = 3

**Q.2)** Find four different solutions of the equation x + 2y = 6.

**Q.3)** Write four solutions for each of the following equations:

(i) Ï€x + y = 9 (ii) 2x + y = 7 (iii) x = 4y

**Q.4) **The bus fare in a town is as follows: For the 1st kilometre, the bus fare is Rs.8 and for the subsequent distance it is Rs.5/km. Let the distance covered be x km and total bus fare be Rs.y. Write a linear equation for the given information, and prepare a graph.

**Q.5) **Vaishaki and Sameera, 2 students of 9th standard, together contributed Rs.200 towards the Relief Fund to help the flood victims. Write a linear equation and draw a graph which satisfies the above data.

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