Question

The graphs of the equations $2x+3y-2=0\mathrm{and}\mathrm{x}-2\mathrm{y}-8=0$ 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 (c).

The given equations are as follows:
$2x+3y-2=0\mathrm{and}\mathrm{x}-2\mathrm{y}-8=0$
They are of the following form:
a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
Here, a₁ = 2, b₁ = 3, c₁ = −2 and a₂ = 1, b₂ = −2 and c₂ = −8
∴ $\frac{a_1}{a_2}=\frac{2}{1},\frac{b_1}{b_2}=\frac{3}{-2}\mathrm{and}\frac{c_1}{c_2}=\frac{-2}{-8}=\frac{1}{4}$
∴ $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
The given system has a unique solution.
Hence, the lines intersect exactly at one point.