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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 and 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, the lines representing the given pair of linear equations are coincident.


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