## 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**

- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.8
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.9
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.10
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.11
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables VSAQS
- RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables MCQS

**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 = λ^{2} 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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