## Pair of Linear Equations in Two Variables Class 10 Solutions Exercise 3.5

### RD Sharma Class 10 Solutions Pair Of Linear Equations In Two Variables Exercise 3.5

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 = λ^{2} and x + λy = 1 have

(i) no solution ?

(ii) infinitely many solutions ?

(iii) a unique solutions ? [NCERT Exemplar]

Solution:

### Pair of Linear Equations in Two Variables Class 10 Solutions Exercise 3.5

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#### RD Sharma Class 10 Solutions

- Pair Of Linear Equations In Two Variables Ex 3.1
- Pair Of Linear Equations In Two Variables Ex 3.2
- Pair Of Linear Equations In Two Variables Ex 3.3
- Pair Of Linear Equations In Two Variables Ex 3.4
- Pair Of Linear Equations In Two Variables Ex 3.5
- Pair Of Linear Equations In Two Variables Ex 3.6
- Pair Of Linear Equations In Two Variables Ex 3.7
- Pair Of Linear Equations In Two Variables Ex 3.8
- Pair Of Linear Equations In Two Variables Ex 3.9
- Pair Of Linear Equations In Two Variables Ex 3.10
- Pair Of Linear Equations In Two Variables Ex 3.11