Chapter 4. Linear Equation In Two Variables
Exercise 4.2
1. Which one of the following options is true, and why?
y = 3x + 5 has
(i) a unique solution, (ii) only two solutions,
Solution
(iii) infinitely many solution, because we can put many value of x and can get many solution of y.
2. Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y
Solution
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)
Solution :
x = 4 + 2y
(i) (0,2)
Putting value of x and y
= 0 = 4 + 2(2)
= 0 = 4 + 4 = 0 = 8, hence it is not a solution of eq
(ii) (2,0)
Putting value of x and y
= 2 = 4 + 2(0) = 2 = 4, hence it is also not a solution of eq
(iii) (4,0)
Putting value of x and y
= 4 = 4 + 2(0) = 4 = 4, hence it is a solution of eq
(v) (1,1)
Putting value of x and y
= 1 = 4 + 2(1) = 1= 6, hence, it is not a solution of eq
4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Solution :
2x + 3y = k
Putting the value of x and y
2(2) + 3(1) = k = 4+3 = k = k = 7
