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## Chapter 4 Linear Equations in Two Variables Exercise 4.2

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

(iii) infinitely many solutions is the correct option as a linear equation in two variables has many solutions i.e. infinite solutions.

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

i) 2x + y = 7

 x 2 1 3.5 0 y 3 5 0 7

ii) πx + y = 9

 x 1 0 -1 9/π y π - 9 9 9 + π 0

iii) x = 4y

 x 0 4 -4 2 y 0 1 -1 1/2

Question 3: Check which of the following are solutions 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)

For i) (0, 2)
x - 2y = 4
= (0) - 2(2) = 4
= 0 - 4 = 4
= -4 ≠ 4

For ii) (2, 0)
x - 2y = 4
= (2) - 2(0) = 4
= 2 - 0 = 4
= 2 ≠ 4

For iii) (4, 0)
x - 2y = 4
= (4) - 2(0) = 4
= 4 - 0 = 4
= 4 = 4

For iv) (√2 , 4√2)
x - 2y = 4
= (√2) - 2(4√2) = 4
= √2 - 8√2 = 4
= -7√2 ≠ 4

For v) (1, 1)
x - 2y = 4
= (1) - 2(1) = 4
= 1 - 2 = 4
= -1 ≠ 4

Therefore option iii) is solution for x - 2y = 4.

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