## Chapter 8 Linear Equations in Two Variables Ex 8.2

**Question 1.**
**Which one of the following options is true and why? y = 3x + 5 has**
**(i) a unique solution**
**(ii) only two solutions**
**(iii) infinitely many solutions**
**Solution:**
**(iii)** A linear equation in two variables has infinitely many solutions.

**Question 2.** **Write four solutions for each of the following equations** **(i) 2x + y = 7** **(ii) πx + y = 9** **(iii) x = 4y** **Solution:**

**(iii)** x = 4y ⇒ x – 4y = 0

**Question 3.**
**Check which of the following are solution of the equation x – 2y = 4 and which are not?**
**(i) (0, 2)**
**(ii) (2,0)**
**(iii) (4,0)**
**(iv) (√2,4√2)**
**(v) (1,1)**
**Solution:**
**(i)** Take x – 2y and put x = 0, y = 2,

we get 0 – 2 x 2 = 0 – 4 = -4 ≠ 4

Hence, (0, 2) is not a solution of x – 2y = 4.
**(ii)** Take x – 2y and put x = 2, y = 0,

we get 2 – 2 x 0 = 2 – 0 = 2 ≠ 4

Hence, (2, 0) is not a solution of x – 2y = 4.

**Take x – 2y and put x = 4, y = 0;**

(iii)

(iii)

we get 4 – 2 x 0 = 4 – 0 = 4

Hence, (4, 0) is a solution of x – 2y = 4.

**Take x – 2y and put x = √2, y = 4√2, we get**

(iv)

(iv)

√2 – 2 x 4√2 = √2 – 8√2 =-7√2 ≠ 4

Hence, (√2,4√2) is not a solution of x – 2y = 4

**Take x – 2y and put x = 1, y = 1,**

(v)

(v)

we get 1 – 2 x 1 = 1 – 2 = -1 ≠ 4

Hence, (1,1) is not a solution of x – 2y = 4.

**Question 4.**
**Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3 y = k.**
**Solution:**

Take 2x + 3y = k

Put x = 2, y = 1 then we get, 2 x 2 + 3 x 1 = k

⇒ 4 + 3 = k

⇒ k = 7