The graphs of the equations $2 x + 3 y - 2 = 0 and x - 2 y - 8 = 0$ are two which are

(a) coincident
(b) parallel
(c) intersecting exactly at one point
(d) perpendicular to each other

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Solution

The correct option is (c).

The given equations are as follows:
$2 x + 3 y - 2 = 0 and x - 2 y - 8 = 0$
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
∴ $\frac{a_{1}}{a_{2}} = \frac{2}{1}, \frac{b_{1}}{b_{2}} = \frac{3}{- 2} and \frac{c_{1}}{c_{2}} = \frac{- 2}{- 8} = \frac{1}{4}$
∴ $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
The given system has a unique solution.
Hence, the lines intersect exactly at one point.

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The graphs of the equations 2x+3y-2=0 and x-2y-8=0 are two which are (a) coincident (b) parallel (c) intersecting exactly at one point (d) perpendicular to each other

The graphs of the equations $2 x + 3 y - 2 = 0 and x - 2 y - 8 = 0$ are two which are

(a) coincident
(b) parallel
(c) intersecting exactly at one point
(d) perpendicular to each other