1. Give the geometric representations of y = 3 as an equation (i) in one variable (ii) in two variables (i) y = 3 [An equation in one variable] ∵ y = 3 is an equation in one variable, i.e. y only. ∴ It has a unique solution y = 3 as shown on the number line shown here. The unique solution is a point. (ii) y = 3 [An equation in two variables] We can write y = 3 as 0.x + y = 3 Now, when x = 1, y = 3 when x = 2, y = 3 when x = 3, y = 3 We get the following table: Plotting the ordered pairs (1, 3), (2, 3) and (3, 3) on a graph paper, we get a line AB as solution of 0 . x + y = 3, i.e. y = 3. 2. Give the geometric representations of 2x + 9 = 0 as an equation (i) in one variable (ii) in two variables : (i) 2x + 9 = 0 [An equation in one variable] We have: 2x + 9 = 0 ⇒ 2x = –9 ⇒ x = (-9/2) which is a linear equation in one variable ‘x’ only. Its solution is the point (-9/2) on the number line as shown below. (ii) 2x + 9 = 0 [An equation in two variables] We can write 2x + 9 = 0 as 2x + 0y + 9 = 0 or 2x = –9 + 0y