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Find the value of k for which the following system of linear equations has infinite solutions: x + (k + 1) y = 5 and (k + 1)x + 9y = 8k – 1
By BYJU'S Exam Prep
Updated on: September 25th, 2023
(a) 3
(b) 1
(c) 2
(d) 4
The value of k for which the following system of linear equations has infinite solutions x + (k + 1)y = 5, (k + 1)x + 9y = 8k – 1 is 2. Given that the system of equations is
x + (k + 1) y = 5 ….. (1)
(k + 1)x + 9y = 8k – 1 …. (2)
Table of content
Comparing the above equations with general form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
Then we get:
a1 = 1, b1 = k + 1, c1 = 5
a2 = k + 1, b2 = 9, c2 = 8k – 1
We know that an infinite number of solutions can exist for a pair of linear equations.
a1/a2 = b1/b2 = c1/c2
1/(k + 1) = (k + 1)/9 = 5/(8k – 1) …. (3)
Consider the first and second terms in(3)
1/(k + 1) = (k + 1)/9
On rearranging we get:
(k + 1)2 = 9
The value of k is:
k + 1 = 3, k + 1 = -3
k = 2, k = -4
Take the first and last (3)
1/(k + 1) = 5/(8k – 1)
On rearranging we get:
5(k + 1) = 8k – 1
5k + 5 = 8k – 1
3k = 6
The value of k is: k = 2
Thus, the given system of equations has an infinite number of solutions when k = 2.
Hence, the correct answer is option C.
Summary:
Find the value of k for which the following system of linear equations has infinite solutions: x + (k + 1) y = 5 and (k + 1)x + 9y = 8k – 1
The value of k for which the following system of linear equations has infinite solutions x + (k + 1)y = 5, (k + 1)x + 9y = 8k – 1 is 2. First-order equations include linear equations. In the coordinate system, linear equations are defined for lines.