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Question 2 (ii)
On comparing the ratios a1a2 , b1b2 and c1c2 , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
9x + 3y + 12 = 0
18x + 6y + 24 = 0

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Solution

9x + 3y + 12 = 0
18x + 6y + 24 = 0
Comparing these equations with,
a1x+b1y+c1=0
a2x+b2y+c2=0
We get,
a1=9,b1=3, and c1=12
a2=18,b2=6 and c2=24
a1a2=918=12
b1b2=36=12 and
c1c2=1224=12
Hence, a1a2=b1b2=c1c2
Therefore, both lines are coincident.

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