RD Sharma Chapter 13 Class 9 Maths Exercise 13.2 Solutions is based on finding the solution of a linear equation. In this exercise, we will explain to students about solving the questions of linear equations efficiently. Let ax+ by + c = 0 where a, b, c are the real numbers, a and b are not equal to zero (a and b ≠ 0), and x, y are the variables, then every pair of values of x and y, which completes the equation is known as a solution of it. Learn about the properties of a linear equation in detail in this article.
Moreover, we have attached the RD Sharma Chapter 13 Class 9 Maths Exercise 13.2 Solutions PDF, which helps students practice for the exam by solving various problems. Start practicing with the problems mentioned in the PDF, which is prepared by our subject experts by RD Sharma, CBSE Text Book, and Previous Year’s Question Paper.
Download RD Sharma Chapter 13 Class 9 Maths Exercise 13.2 Solutions PDF
Important Definitions RD Sharma Chapter 13 Class 9 Maths Exercise 13.2 Solutions
In the following points, we have given the complete information about finding the solution of a linear equation.
A solution 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.
Example of A Solution of Linear Equations in Two Variables
5p + 3q = 30
= The above equation has two variables namely p and q.
= Graphically, this equation can be described by replacing the variables to zero.
= The value of p when q = 0 is
= 5p + 3(0) = 30
= p = 6
= and the value of q when p = 0 is,
= 5 (0) + 3q = 30
= q = 10
For the given linear equations in two (2) variables, the solution would be unique for both the equations, only if they cross at a single point.
The circumstance to get the unique solution for the provided linear equations is the hill of the line determined by the two equations, respectively, should not be equal.
Suppose n1 and n2 are two slopes of equations of two lines in two variables. Therefore, if the equations have a unique solution, then-
n1 ≠ n2
If the two linear equations have equivalent slope values, then the equations will have no solutions.
n1 = n2
This is because the lines are parallel to one another and do not meet.
Examples of RD Sharma Chapter 13 Class 9 Maths Exercise 13.2 Solutions
Ques- If p = 1 and q = 6 is a solution of the equation 8p – aq + a2 = 0, find the values of a.
Given, ( 1 , 6 ) is the solution of an equation 8p – aq + a2 = 0
= Substituting p = 1 and q = 6 in 8p – aq + a2 = 0, we get
= 8 x 1 – a x 6 + a2 = 0
= a2 – 6a + 8 = 0 (a quadratic equation)
= By using quadratic factorization
= a2 – 4a – 2a + 8 = 0
= a (a – 4) – 2 (a – 4) = 0
= (a – 2) (a – 4)= 0
= a = 2 and 4
= Values of ‘a’ are 2 and 4.
Ques- Find the value of λ, if a = –λ and b = 5/2 is a solution of the equation a + 4b – 7 = 0
Given, (-λ, 5/2) is the solution of equation 3a + 4b= k
= Substituting a = – λ and b = 5/2 in a + 4b – 7 = 0, we get
= – λ + 4 (5/2) – 7 =0
= – λ + 10 – 7 = 0
= λ = 3