20. The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be

a) parallel lines
(b) coincident lines
(c) intersecting lines
(d) perpendicular lines
Answer: (a) parallel lines
Explanation:
Given pair of equations are 4x + 3y – 1 = 5 and 12x + 9y = 15.
Comparing with the standard form,
a₁ = 4, b₁ = 3, c₁ = -6
a₂ = 12, b₂ = 9, c₂ = -15
a₁/a₂ = 4/12 = 1/3
b₁/b₂ = 3/9 = 1/3
c₁/c₂ = -6/-15 = 2/5
Thus, a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Hence, the given pair of equations has no solution.
That means, the lines representing the given pair of equations are parallel to each other.