(i) intersecting lines (ii) parallel lines (iii) coincident lines

**Solution:**

**(i) Given, 2x + 3y – 8 = 0.**

To find another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines, it should satisfy below condition;

(a_{1}/a_{2}) ≠ (b_{1}/b_{2})

Thus, another equation could be 2x – 7y + 9 = 0, such that;

(a_{1}/a_{2}) = 2/2 = 1 and

(b_{1}/b_{2}) = 3/-7

Clearly, we can see another equation satisfies the condition.

**(ii) Given, 2x + 3y – 8 = 0.**

To find another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines, it should satisfy below condition;

(a_{1}/a_{2}) = (b_{1}/b_{2}) ≠ (c_{1}/c_{2})

Thus, another equation could be 6x + 9y + 9 = 0, such that;

(a_{1}/a_{2}) = 2/6 = 1/3

(b_{1}/b_{2}) = 3/9= 1/3

(c_{1}/c_{2}) = -8/9

Clearly, we can see another equation satisfies the condition.

**(iii) Given, 2x + 3y – 8 = 0.**

To find another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines, it should satisfy below condition;

(a_{1}/a_{2}) = (b_{1}/b_{2}) = (c_{1}/c_{2})

Thus, another equation could be 4x + 6y – 16 = 0, such that;

(a_{1}/a_{2}) = 2/4 = 1/2

(b_{1}/b_{2}) = 3/6 = 1/2

(c_{1}/c_{2}) = -8/-16 = 1/2

Clearly, we can see another equation satisfies the condition.