## Revision Notes of Ch 4 Linear Equations in Two Variables Class 9th Math

**Topics in the Chapter**

- Linear equation in two variables
- Solution of a linear equation in two variables
- Representation of a linear equation in two variables graphically.
- Graphical solution of linear equation in two variables
- Represent the equation 2y + 5 = 0, on Cartesian plane.

**Linear equation in two variables**

An equation of the form, ax + by + c = 0, where a, b and c are constants, such that a and

b are both not zero and x and y are variables is called a linear equation in two variables.

For example, 2x + 3y + 10 = 0, 3x + 7y = 0

Real life situations can be expressed mathematically as linear equations in two variables.

Example:The age of Ram is 3 more than twice the age of Mohan. Write a linear equation in two

variables to represent this statement.

Solution:

Let the age of Mohan be x years and the age of Ram be y years.

Thus, the given condition can be expressed as y = 2x + 3

**Solution of a linear equation in two variables**

• The values of the variables in a linear equation, which satisfy the equation are the solutions of

that linear equation.

• A linear equation in two variables has infinitely many solutions.

• Solution of linear equation in two variables can be found by substitution method.

**Example:**

Find two different solutions of the equation 4x + 5y = 20.

**Solution:**

Given equation is 4x + 5y = 20.

If we take x = 0, we obtain:

4 × 0 + 5y = 20

⇒ 5y = 20

⇒ y = 4

So, (0, 4) is a solution of the given equation.

If we take y = 0, we obtain:

4x + 5 × 0 = 20

⇒ 4x = 20

⇒ x = 5

So, (5, 0) is a solution of the given equation.

**Representation of a linear equation in two variables graphically.**

The geometrical representation of the linear equation, ax + by + c = 0, is a straight line.

In order to represent a linear equation in two variables graphically, its two or three different

points are calculated and then the corresponding points are plotted and joined on the

coordinate plane.

**Example:**

Represent x + 3y = 6 on a graph paper.

**Graphical solution of linear equation in two variables**

and moreover, every solution of the linear equation is a point on the graph of the linear equation.

**Example:**A bag contains some Re 1 coins and some Rs 2 coins. The total worth of coins is Rs 45. Find the

number of Re 1 coins, if there are 10 coins of Rs 2.

**Solution:**

Let there be x coins of Re 1 and y coins of Rs 2.

Thus, 1x + 2y = 45

⇒ x + 2y = 45

This is the required linear equation of the given information. The three solutions of this equation

have been given in the tabular form as follows:

From the above graph, it can be seen that the value of x corresponding to y = 10 is 25.

Therefore, there are 25 coins of Re 1, if there are 10 coins of Rs 2.

The graph of x = a is a straight line parallel to the y-axis, situated at a distance of a units

from y-axis.

The graph of y = b is a straight line parallel to the x-axis, situated at a distance of b units

from x-axis.

Thus, 1x + 2y = 45

⇒ x + 2y = 45

This is the required linear equation of the given information. The three solutions of this equation

have been given in the tabular form as follows:

From the above graph, it can be seen that the value of x corresponding to y = 10 is 25.

Therefore, there are 25 coins of Re 1, if there are 10 coins of Rs 2.

The graph of x = a is a straight line parallel to the y-axis, situated at a distance of a units

from y-axis.

The graph of y = b is a straight line parallel to the x-axis, situated at a distance of b units

from x-axis.

**Example:**
Represent the equation 2y + 5 = 0, on Cartesian plane.

**Solution**