# CBSE Class 9 Maths Revision Notes Chapter 4

## Class 9 Maths Revision Notes for Linear Equations in Two Variables of Chapter 4

Extramarks Revision Notes provide clear and concise pointers for Class 9 Mathematics Chapter 4 Linear Equations in Two Variables. It contains all the equations and their description in an organised manner so that it is easy for students to revise the chapters before examinations and recall them better.

## Class 9 Maths Revision Notes for Linear Equations in Two Variables of Chapter 4

### Solution of Linear Equation:

A linear equation has a unique solution when there exists only one point exists that satisfies the linear equation.

For example: Solution of 2x+6=2 is

2x+6=2

2x=2−6

2x=−4

x=−42

x=−2

Because 2x+6=2 has just one variable, x, it has a unique solution. Geometrically, it will be a point on rectangular axes with an ordinate of 0.

When a system of lines intersects at only one place, it has a unique solution.

A linear equation in two variables with infinitely many solutions suggests that there are more than one ordered pair that satisfies the equation.

For example: Solution of 2x+3y=12 are

 X 3 0 6 Y 2 4 0

The following value (3,2), (0,4), (6,0) of x and y satisfies the equation 2x+3y=12 therefore they are the solutions of 2x+3y=12.

A system of linear equations has an unlimited number of solutions if the system of lines coincides, which means that each point on the system of lines is the solution.

For example, the system of linear equations 6x+4y=2 and 3x2y=1 has an infinite number of solutions because these two lines meet on a graph.

### Graph of Linear Equation in Two Variables:

A linear equation with two variables is known to have an infinite number of solutions, each of which is represented by a set of two numbers.

As a result, we can plot these values on a coordinate plane and create a graph of a linear equation with two variables.

### Equations of Line Parallel to X-axis and Y-axis:

• A linear equation with two variables has the form ax+by+c=0. The equation becomes ax+c=0 when we replace y=0. The graph of the equation ax+c=0 is a straight line that is perpendicular to the y-axis.
• The equation becomes by+c=0 if x=0 is substituted in ax+by+c=0.
• The graph of the equation by+c=0 is a straight line that is perpendicular to the x-axis.
• The x-axis equation is y=0 because y-coordinates are always zero on the x-axis and the coordinate form of any point on the x-axis is (x,0).
• The y-axis equation is x=0 because x-coordinates are always zero on the y-axis and the coordinate form of any point on the y-axis is (0,y).
• If the value of x in a coordinate point (x,y) is positive, the point will be on the right side of the y-axis; if it is negative, the point will be on the left side of the y-axis.
• Similarly, if y is a positive constant, the point will be on the upper side of the x-axis, and if it is a negative constant, the point will be on the lower side of the x-axis.

### 1. Give an overview of the chapter.

“Linear Equations in Two Variables” is Chapter 4 of the NCERT Textbook and is part of Unit 2 Algebra. This chapter will teach students about the Graph of a Linear Equation in Two Variables and Equations of Lines Parallel to the x-axis and y-axis by displaying the two variables of a linear equation on a graph sheet. The solutions for all of these topics are supplied step-by-step so that the learner can internalise the notion gradually.

### 2. What is the linear equation in the two variables?

A linear equation is one that has two variables and produces a straight line. To confirm that the equation holds, the values of the unknown variables must be determined. The sign of ‘=’ in the equation helps in determining the values of the variables, where the right side of the equation equals the left side. The equation is written as Mx + Ny = C. The numbers in the question are represented by M, N, and C.

### 3. How do you solve linear equations in two variables?

When a linear equation is plotted on a graph, it produces a straight line. The equation is made up of variables and coefficients. A linear equation has the formula Ax + By = C. A, B, and C are real numbers, whereas x and y are variables whose values are unknown. One pair of x and y will satisfy the equation. Find the equivalent y value for a given x value. Then, for y, select a value and get the equivalent value of x. Make a graph of it. Repeat these steps 3–4 times. The solution will be the location where the two lines intersect.

### 4. Can the graph of a linear equation with two variables be a curve?

No, the graph of a two-variable linear equation cannot be a curve. The path is always straight. Extramarks Revision Notes or additional NCERT Class 9 Maths Chapter 4 questions that will assist you in completing comprehensive exercises along with examples and random questions.