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Question

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

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Solution

The correct option is (c).

The given equations are as follows:
2x+3y-2=0 and x-2y-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
a1a2=21,b1b2=3-2andc1c2=-2-8=14
a1a2b1b2
The given system has a unique solution.
Hence, the lines intersect exactly at one point.

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