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

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)

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:

(i)

(ii)

(iii) –2x + 3y = 6

(iv) x = 3y

(v) 2x = –5y

(vi) 3x + 2 = 0
(vii) y – 2 = 0

(viii) 5 = 2x

Write four solutions for each of the following equations:

(i) 2x + y = 7

(ii)

(iii) x = 4y

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)

(v) (1, 1)