Linear Equations in Two Variables
Exercise 4.1
1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be Rs x and that of a pen to be Rs y).
(i) \(2x + 3y =9.\bar{35}\)
(ii) \(x –\frac{y}{5} – 10 = 0\)
(iii) \(–2x + 3y = 6\)
(iv) \(x = 3y\)
(v) \(2x = –5y\)
(vi) \(3x + 2 = 0\)
(vii) \(y – 2 = 0\)
(viii) \(5 = 2x\)
Linear Equations 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,
(iii) infinitely many solutions.
2. Write four solutions for each of the following equations:
(i) \(2x + y = 7\)
(ii) \(πx + y = 9\)
(iii) \(x = 4y\)
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) \((\sqrt{2}, 4\sqrt{2})\) (v) (1, 1)
4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.