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Question

Consider two equations in the variables x and y written in the standard form:
5x+6y+4=0 and
10x+12y+7=0
What is the nature of these two lines?

A
Coincident
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B
Intersecting
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C
Parallel
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D
Coincident or parallel
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Solution

The correct option is C Parallel
The equations of the two lines are:

5x+6y+4=0
10x+12y+7=0

Here,
a1=5,b1=6,c1=4,a2=10,b2=12,c2=7.

a1a2=510=12

b1b2=612=12

c1c2=47.

a1a2=b1b2c1c2.

The pair of equations have no solutions, i.e, they are parallel.

Also, when we plot the graphs of these two equations, it is visible that they are parallel to each other.


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