text: ## RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5
  
  These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5
  
  Other Exercises
  
  In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : (1 – 4)
  Question 1.
  x – 3y = 3
  3x – 9y = 2 (C.B.S.E. 1994)
  Solution:
  
  Question 2.
  2x + y = 5
  4x + 2y = 10 (C.B.S.E. 1995C)
  Solution:
  
  Question 3.
  3x – 5y = 20
  6x – 10y = 40 (C.B.S.E. 1993)
  Solution:
  
  Question 4.
  x – 2y = 8
  5x – 10y = 10 (C.B.S.E. 1993)
  Solution:
  
  Find the value of k for which the following system of equations has a unique solution: (5 – 8)
  Question 5.
  kx + 2y = 5
  3x + y = 1 (C.B.S.E. 1990C, 92C)
  Solution:
  
  Question 6.
  4x + ky + 8 = 0
  2x + 2y + 2 = 0 [NCERT]
  Solution:
  
  Question 7.
  4x – 5y = k
  2x – 3y = 12
  Solution:
  
  Question 8.
  x + 2y = 3
  5x + ky + 7 = 0
  Solution:
  
  Find the value of k for which each of the following systems of equations have infinitely many solution : (9 – 19)
  Question 9.
  2x + 3y – 5 = 0
  6x + ky – 15 = 0 (C.B.S.E. 1991)
  Solution:
  
  Question 10.
  4x + 5y = 3
  kx + 15y = 9 (C.B.S.E. 1990C)
  Solution:
  
  Question 11.
  kx – 2y + 6 = 0
  4x – 3y + 9 = 0
  Solution:
  
  Question 12.
  8x + 5y = 9
  kx + 10y = 18 (C.B.S.E. 1999)
  Solution:
  
  Question 13.
  2x – 3y = 7
  (k + 2) x + (2k + 1) y = 3 (2k – 1) (C.B.S.E. 1999)
  Solution:
  
  Question 14.
  2x + 3y = 2
  (k + 2)x + (2k + 1) y = 2 (k – 1) (C.B.S.E. 2000, 2003)
  Solution:
  
  Question 15.
  x + (k + 1) y = 4
  (k + 1) x + 9y = 5k + 2 (C.B.S.E. 2000C)
  Solution:
  
  Question 16.
  kx + 3y = 2k + 1
  2(k+ 1) x + 9y = 7k + 1 (C.B.S.E. 2000C)
  Solution:
  
  Question 17.
  2x + (k – 2) y = k
  6x + (2k – 1) y = 2k + 5 (C.B.S.E. 2000C)
  Solution:
  
  Question 18.
  2x + 3y = 7
  (k + 1) x + (2k – 1)y = 4k + 1 (C.B.S.E. 2001)
  Solution:
  
  Question 19.
  2x + 3y = k
  (k – 1) x + (k + 2) y = 3k (C.B.S.E. 2001)
  Solution:
  
  Find the value of k for which the following system of equations has no solution : (20 – 25) :
  Question 20.
  kx – 5y = 2
  6x + 2y = 1 (C.B.S.E. 1994C)
  Solution:
  
  Question 21.
  x + 2y = 0
  2x + ky = 5 (C.B.S.E. 1993C)
  Solution:
  
  Question 22.
  3x – 4y + 7 = 0
  kx + 3y – 5 = 0 (C.B.S.E. 1996)
  Solution:
  
  Question 23.
  2x – ky + 3 = 0
  3x + 2y – 1 = 0 (C.B.S.E. 1996)
  Solution:
  
  Question 24.
  2x + ky = 11
  5x – 7y = 5 (C.B.S.E. 1995)
  Solution:
  
  Question 25.
  kx + 3y = 3
  12x + ky = 6
  Solution:
  
  Question 26.
  For what value of k, the following system of equations will be inconsistant ?
  4x + 6y = 11
  2x + ky = 1 (C.B.S.E. 1994C)
  Solution:
  
  Question 27.
  For what value of a, the system of equations
  αx + 3y = α – 3
  12x + αy = α
  will have no solution. (C.B.S.E. 2003)
  Solution:
  
  Question 28.
  Find the value of k for which the system
  kx + 2y = 5
  3x + y = 1
  has (i) a unique solution, and (ii) no solution.
  Solution:
  
  k = 6
  
  Question 29.
  Prove that there is a value of c (≠ 0) for which the system
  6x + 3y = c – 3
  12x + cy = c
  has infinitely many solutions. Find this value.
  Solution:
  
  Question 30.
  Find the values of k for which the system
  2x + k y = 1
  3x – 5y = 7
  will have (i) a unique solution, and (ii) no solution.
  Is there a value of k for which the system has infinitely many solutions?
  Solution:
  
  Question 31.
  For what value of k, the following system of equations will represent the coincident lines ?
  x + 2y + 7 = 0
  2x + ky + 14 = 0 (C.B.S.E. 1992)
  Solution:
  
  Question 32.
  Obtain the condition for the following system of linear equations to have a unique solution
  ax + by = c
  lx + my = n (C.B.S.E. 1991C)
  Solution:
  
  Question 33.
  Determine the values of a and b so that the following system of linear equations have infinitely many solutions ?
  (2a – 1) x + 3y – 5 = 0
  3x + (b – 1) y – 2 = 0 (C.B.S.E. 2001C)
  Solution:
  
  Question 34.
  Find the values of a and b for which the following system of linear equations has infinite number of solutions :
  2x – 3y = 7
  (a + b) x – (a + b – 3) y = 4a + b (C.B.S.E. 2002)
  Solution:
  
  Question 35.
  Find the values of p and q for which the following system of linear equations has infinite number of solutions:
  2x + 3y = 9
  (p + q) x + (2p – q) y = 3 (p + q + 1)
  Solution:
  
  Question 36.
  Find the value of a and b for which the following system of equations has infinitely many solutions :
  (i) (2a – 1) x – 3y = 5
  3x + (b – 2) y = 3 (C.B.S.E. 2002C)
  (ii) 2x – (2a + 5) y = 5
  (2b + 1) x – 9y = 15 (C.B.S.E. 2002C)
  (iii) (a – 1) x + 3y = 2
  6x + (1 – 2b) y = 6 (C.B.S.E. 2002C)
  (iv) 3x + 4y = 12
  (a + b) x + 2 (a – b) y = 5a – 1 (C.B.S.E. 2002C)
  (v) 2x + 3y = 7
  (a – b) x + (a + b) y = 3a + b – 2
  (vi) 2x + 3y – 7 = 0 [CBSE 2010]
  (a – 1) x + (a + 1) y = (3a – 1)
  (vii) 2x + 3y = 7
  (a – 1) x + (a + 2) y = 3a [CBSE 2010]
  (viii) x + 2y = 1
  (a – b) x + (a + b) y = a + b – 2 [NCERT Exemplar]
  (ix) 2x + 3y = 7
  2ax + ay = 28 – by [NCERT Exemplar]
  Solution:
  
  Question 37.
  For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have
  (i) no solution ?
  (ii) infinitely many solutions ?
  (iii) a unique solutions ? [NCERT Exemplar]
  Solution:
  
  Hope given RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 are helpful to complete your math homework.
  
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