Question

The graphs of the equations $5x-15y=8\mathrm{and}3x-9y=\frac{24}{5}$ are two which are
(a) coincident
(b) parallel
(c) intersecting exactly at one point
(d) perpendicular to each other

Answer 1

The correct option is (a).

The given system of equations can be written as follows:
$5x-15y-8=0\mathrm{and}3\mathrm{x}-9\mathrm{y}-\frac{24}{5}=0$
The given equations are of the following form:
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
Here, a₁ = 5, b₁ = −15, c₁ = −8 and a₂ = 3, b₂ = −9 and c₂ = $-\frac{24}{5}$
∴ $\frac{a_1}{a_2}=\frac{5}{3},\frac{b_1}{b_2}=\frac{-15}{-9}=\frac{5}{3}\mathrm{and}\frac{c_1}{c_2}=-8\times \frac{5}{-24}=\frac{5}{3}$
∴ $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
The given system of equations will have an infinite number of solutions.
Hence, the lines are coincident.