Q2 of 44 Page 3

Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:

(2a - 1)x + 3y = 5, 3x + (b - 1)y = 2. (CBSE 2001)

Given: (2a - 1)x + 3y = 5 – eq 1


3x + (b - 1)y = 2 – eq 2


Here,


a1 = (2a - 1), b1 = 3, c1 = - 5


a2 = 3 , b2 = (b - 1), c2 = - 2


Given that system of equations has infinitely many solution


∴ = =


= =


Here,


=


- 2×(2a - 1) = 3×( - 5)


- 4a + 2 = - 15


- 4a = - 15 - 2


- 4a = - 17


b =


∴ b = -


Also,


=


3( - 2) = - 5×(b - 1)


- 6 = - 5b + 5


5b = 5 + 6


5b = 11


b =


∴b =


∴ a = , b =

More from this chapter

All 44 →
1

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

2x + (k – 2)y = k,


6x + (2k – 1)y = (2k + 5). (CBSE 2000)

 3

Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:

2x + 3y = 7, (a + b)x + (2a - b)y = 21. (CBSE 2001)

 4

Find the values of a and b for which each of the following systems of linear equations has an infinite number of solutions:

2x + 3y = 7, 2ax + (a + b)y = 28 (CBSE 2001)

 5

Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

(k – 1)x – y = 5,


(k + 1)x + (1 – k)y = (3k + 1) . (CBSE 2003)