Class 10 Exam > Class 10 Questions > For what value of k, the following pair of li...
Start Learning for Free
For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).?
Most Upvoted Answer
For what value of k, the following pair of linear equations has infini...
Community Answer
For what value of k, the following pair of linear equations has infini...
Explanation:
To have an infinite number of solutions, the given pair of equations should be consistent and dependent. In other words, the two equations should represent the same line or plane in 2D or 3D space respectively.
Let's check if the given equations satisfy these conditions:
Step 1: Convert the equations into slope-intercept form y = mx + b
Equation 1: 2x - (k - 1)y = k
(k - 1)y = 2x - k
y = 2/k x - 1/(k - 1)
Equation 2: 6x - (2k - 1)y = 2k + 5
(2k - 1)y = 6x - (2k + 5)
y = 6/(2k - 1) x - (2k + 5)/(2k - 1)
Step 2: Equate the slopes and y-intercepts of the two equations
2/k = 6/(2k - 1)
-1/(k - 1) = -(2k + 5)/(2k - 1)
Step 3: Solve for k
From the first equation, we get:
4k - 2 = 6k
k = -2
Substituting this value of k in the second equation, we get:
-1/(-2 - 1) = -(2(-2) + 5)/(2(-2) - 1)
1/3 = -1/5
This is a contradiction, which means that the given equations do not have an infinite number of solutions for any value of k.
Therefore, there is no value of k for which the given pair of linear equations has an infinite number of solutions.
To have an infinite number of solutions, the given pair of equations should be consistent and dependent. In other words, the two equations should represent the same line or plane in 2D or 3D space respectively.
Let's check if the given equations satisfy these conditions:
Step 1: Convert the equations into slope-intercept form y = mx + b
Equation 1: 2x - (k - 1)y = k
(k - 1)y = 2x - k
y = 2/k x - 1/(k - 1)
Equation 2: 6x - (2k - 1)y = 2k + 5
(2k - 1)y = 6x - (2k + 5)
y = 6/(2k - 1) x - (2k + 5)/(2k - 1)
Step 2: Equate the slopes and y-intercepts of the two equations
2/k = 6/(2k - 1)
-1/(k - 1) = -(2k + 5)/(2k - 1)
Step 3: Solve for k
From the first equation, we get:
4k - 2 = 6k
k = -2
Substituting this value of k in the second equation, we get:
-1/(-2 - 1) = -(2(-2) + 5)/(2(-2) - 1)
1/3 = -1/5
This is a contradiction, which means that the given equations do not have an infinite number of solutions for any value of k.
Therefore, there is no value of k for which the given pair of linear equations has an infinite number of solutions.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).?
Question Description
For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).?.
For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).?.
Solutions for For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? defined & explained in the simplest way possible. Besides giving the explanation of
For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).?, a detailed solution for For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? has been provided alongside types of For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? theory, EduRev gives you an
ample number of questions to practice For what value of k, the following pair of linear equations has infinite number of solutions:2x + (k - 1)y = k; 6x + (2k - 1)y = (2k + 5).? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup