Question

The graphic representation of the equations $x+2y=3\mathrm{and}2\mathrm{x}+4\mathrm{y}+7=0$ gives a pair of
(a) parallel lines
(b) intersecting lines
(c) coincident lines
(d) none of these

Answer 1

The correct option is (a).

The given system of equations can be written as follows:
x + 2y − 3 = 0 and 2x + 4y + 7 = 0
The given equations are of the following form:
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
Here, a₁ = 1, b₁ = 2, c₁ = −3 and a₂ = 2, b₂ = 4 and c₂ = 7
∴ $\frac{a_1}{a_2}=\frac{1}{2},\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\mathrm{and}\frac{c_1}{c_2}=\frac{-3}{7}$
∴ $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
So, the given system has no solution.
Hence, the lines are parallel.