RD Sharma Chapter 13 Class 9 Maths Exercise 13.1 Solutions is based on the introduction of linear equations in two variables. This exercise deals with the equations with degree one, which is called the linear equations. ax + by + c = 0 is the standard pattern of a linear equation in two variables (where a and b are real numbers & a and b are not equal to 0). In the linear equation, a similar number can be added or deducted from both sides of the equation, and both sides can be divided or multiplied by an equal non-zero number.
Moreover, we have attached the RD Sharma Chapter 13 Class 9 Maths Exercise 13.1 Solutions PDF, which helps students practice for the exam with various questions related to this exercise. As the PDF is prepared by our experts with the stepwise solution to each question mentioned. Practicing with the different types of problems help learners to score well in the exam.
Learn about RD Sharma Chapter 13 (Linear Equations In Two Variables) Class 9
Download RD Sharma Chapter 13 Class 9 Maths Exercise 13.1 Solutions PDF
Solutions for Class 9 Maths Chapter 13 Linear Equations in Two Variables Exercise 13.1
Important Definitions RD Sharma Chapter 13 Class 9 Maths Exercise 13.1 Solutions
Definition of Linear Equation in two variables
An equation is stated to be a linear equation in two variables if it is formulated in the form of ax + by + c=0, where a, b, & c are the real numbers and coefficients of x & y, i.e., a & b, respectively, are not equal to zero.
Example of linear equations in two variables
10x + 4y = 3 and -x + 5y = 2
The solution for such an equation is a set of values, one for x and another for y, which further creates the two sides of an equation equal.
Solutions of Linear Equations in Two Variables
A solution of a linear equation in two variables, ax + by = c, is a particular spot in the graph. When x-coordinate is multiplied by ‘a’ and y-coordinate is multiplied by ‘b.’ The total of these two conditions will be equal to ‘c.’
Fundamentally, for a linear equation in two variables, there are infinitely various solutions.
Examples of RD Sharma Chapter 13 Class 9 Maths Exercise 13.1 Solutions
Express the below mentioned linear equations in the form ax + by + c = 0 and indicate the values of a, b, & c in each case-
(a) -2x + 3y = 12
(b) x – y/2 – 5 = 0
(c) 2x + 3y = 9.35
(d) 3x = -7y
(e) 2x + 3 = 0
(f) y – 5 = 0
(g) 4 = 3x
(h) y = x/2
Solution:
(a) -2x + 3y = 12
Or – 2x + 3y – 12 = 0
By Comparing the equation with ax + by + c = 0
a = – 2; b = 3; c = -12
(b) x – y/2 – 5= 0
By Comparing the equation with ax + by + c = 0 ,
a = 1; b = -1/2, c = -5
(c) 2x + 3y = 9.35
or 2x + 3y – 9.35 =0
By Comparing the equation with ax + by + c = 0
a = 2 ; b = 3 ; c = -9.35
(d) 3x = -7y
or 3x + 7y = 0
By Comparing the equation with ax+ by + c = 0,
a = 3 ; b = 7 ; c = 0
(e) 2x + 3 = 0
or 2x + 0y + 3 = 0
By Comparing the equation with ax + by + c = 0,
a = 2 ; b = 0 ; c = 3
(f) y – 5 = 0
or 0x + y – 5 = 0
By Comparing the equation with ax + by+ c = 0,
a = 0; b = 1; c = -5
(g) 4 = 3x
or 3x + 0y – 4 = 0
By Comparing the equation with ax + by + c = 0,
a = 3; b = 0; c = -4
(h) y = x/2
Or x – 2y = 0
Or x – 2y + 0 = 0
By Comparing the equation with ax + by + c = 0 ,
a = 1; b = -2; c = 0