## RS Aggarwal Class 10 Solutions Chapter 3 Linear equations in two variables Ex 3D

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3D.

### RS Aggarwal Solutions Class 10 Chapter 3

- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3A
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3B
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3C
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3D
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3E
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3F
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables MCQS
- RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Test Yourself

**Show that each of the following systems of equations has a unique solution and solve it:**

**Question 1.**

**3x + 5y = 12, 5x + 3y = 4**

**Solution:**

**Question 2.**

**2x – 3y = 17, 4x + y = 13.**

**Solution:**

**Question 3.**

** + = 3, x – 2y = 2**

**Solution:**

This system has a unique solution.

From (ii), x = 2 + 2y

Substituting the value of x in (i),

2(2 + 2y) + 3y = 18

=> 4 + 4y + 3y = 18

=> 7y = 18 – 4 = 14

=> y = 2

and x = 2 + 2 x 2 = 2 + 4 = 6

x = 6, y = 2

**Find the value of k for which each of the following systems of equations has a unique solution:**

**Question 4.**

**2x + 3y – 5 = 0, kx – 6y – 8 = 0.**

**Solution:**

**Question 5.**

**x – ky = 2, 3x + 2y + 5 = 0.**

**Solution:**

**Question 6.**

**5x – 7y – 5 = 0, 2x + ky – 1 = 0.**

**Solution:**

**Question 7.**

**4x + ky + 8 = 0, x + y + 1 = 0.**

**Solution:**

**Question 8.**

**4x – 5y = k, 2x – 3y = 12.**

**Solution:**

**Question 9.**

**kx + 3y = (k – 3), 12x + ky = k.**

**Solution:**

**Question 10.**

**Show that the system of equations 2x – 3y = 5, 6x – 9y = 15 has an infinite number of solutions.**

**Solution:**

**Question 11.**

**Show that the system of equations 6x + 5y = 11, 9x + y = 21 has no solution.**

**Solution:**

**Question 12.**

**For what value of k does the system of equations kx + 2y = 5, 3x – 4y = 10 have**

**(i) a unique solution,**

**(ii) no solution?**

**Solution:**

**Question 13.**

**For what value of k does the system of equations x + 2y = 5, 3x + ky + 15 = 0 have**

**(i) a unique solution,**

**(ii) no solution?**

**Solution:**

**Question 14.**

**For what value of k does the system of equations x + 2y = 3, 5x + ky + 7 = 0 have**

**(i) a unique solution,**

**(ii) no solution? Also, show that there is no value of k for which the given system of equations has infinitely many solutions.**

**Solution:**

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

**Question 15.**

**2x + 3y = 7,**

**(k – 1) x + (k + 2) y = 3k. [CBSE 2010]**

**Solution:**

**Question 16.**

**2x + (k – 2 ) y = k,**

**6x + (2k – 1) y = (2k + 5). [CBSE 2000C]**

**Solution:**

**Question 17.**

**kx + 3y = (2k+ 1),**

**2(k + 1) x + 9y = (7k + 1). [CBSE 2000C]**

**Solution:**

**Question 18.**

**5x + 2y = 2k,**

**2(k + 1) x + ky = (3k + 4). [CBSE 2003C]**

**Solution:**

**Question 19.**

**(k – 1) x – y = 5**

**(k + 1) x + (1 – k) y = (3k + 1) [CBSE 2003]**

**Solution:**

**Question 20.**

**(k – 3) x + 3y = k,**

**kx + ky = 12.**

**Solution:**

=> k (k – 6) = 0

Either k = 0, which is not true, or k – 6 = 0, then k = 6

k = 6

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

**Question 21.**

**(a – 1) x + 3y = 2,**

**6x + (1 – 2b) y = 6. [CBSE 2002C]**

**Solution:**

**Question 22.**

**(2a – 1) x + 3y = 5,**

**3x + (6 – 1) y = 2. [CBSE 2001C]**

**Solution:**

**Question 23.**

**2x – 3y = 7,**

**(a + b) x – (a + b – 3) y = 4a + b. [CBSE 2002]**

**Solution:**

**Question 24.**

**2x + 3y = 7,**

**(a + b + 1) x + (a + 2b + 2) y – 4(a + b) + 1. [CBSE 2003]**

**Solution:**

**Question 25.**

**2x + 3y = 7,**

**(a + b) x + (2a – b) y = 21. [CBSE 2001]**

**Solution:**

**Question 26.**

**2x + 3y = 7,**

**2ax + (a + b) y = 28. [CBSE 2001]**

**Solution:**

**Find the value of k for which each of the following systems of equations has no solution:**

**Question 27.**

**8x + 5y = 9, kx + 10y = 15.**

**Solution:**

**Question 28.**

**kx + 3y = 3, 12x + ky = 6.**

**Solution:**

kx + 3y = 3

12x + ky = 6

**Question 29.**

**3x – y – 5 = 0, 6x – 2y + k = 0 (k ≠ 0). [CBSE 2008]**

**Solution:**

**Question 30.**

**kx + 3y = k – 3, 12x + ky = k. [CBSE 2009]**

**Solution:**

**Question 31.**

**Find the value of k for which the system of equations 5x – 3y = 0, 2x + ky = 0 has a nonzero solution.**

**Solution:**

Hope given RS Aggarwal Solutions Class 10 Chapter 3 Linear equations in two variables Ex 3D are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Amit Bilung says

It’s very nice.

Harsh says

I the question number 4 the equation is kx-6x-8=0 , than why is the value of c2 = -6

Harsh says

Plz recheck the question 5