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,andc1=12 a2=18,b2=6andc2=24 a1a2=918=12 b1b2=36=12 and c1c2=1224=12 Hence, a1a2=b1b2=c1c2 Therefore, both lines are coincident.