Class 9, Maths, Chapter 4, Exercise 4.2, Solutions
Q.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
Ans: Given equation is y = 3 x + 5
Let x=1, y = 3(1) + 5 = 3 + 5 = 8
Let x=2, y = 3 (2) + 5 = 6 + 5 = 11
Let x=3, y = 3 (3) + 5 = 9 + 5 = 14
Clearly, for different values of x, we get another value of y. Thus, the chosen value of x together with this value of y constitutes another solution of the given solution. So, there is no end to different solutions of a linear equation in two variables.
Therefore, the correct answer is option (iii) i.e., infinitely many solutions.
Q.2. Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y
Ans:
Q.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) $\left( \sqrt{2},4\sqrt{2} \right)$
(v) (1, 1)
Ans:
Q.4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
Ans:
