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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) \(5 = 2x\)

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.