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Question 2. On comparing the ratios a1/a2 , b1/b2 and c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

Question 2. On comparing the ratios a1/a2 , b1/b2  and c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
Use this table for the solution

 S.N. Compare the Ratio Graphic representation Algebraic interpretation Linear equations 1 Intersection lines at one point Exactly one solution or unique solution Consistent 2 Coincident line Infinity solution or many solutions Dependent and consistent 3 Parallel lines No solution Inconsistent

Solution: (i)

5x – 4y + 8         = 0

7x + 6y – 9         = 0
Compare the equation with

We get
a1 = 5,            b1       = -4,               and c1 = 8
a2 =7               b2       =6                    and c2 = -9

Hence

So both are Intersecting lines at one point
(ii)9x + 3y + 12            = 0
18x + 6y + 24           = 0
Compare the equation with

We get
a1 = 9,           b1       = 3,                 and c1 = 12
a2 =18          b2        =6,                   and c2 = 24

Hence

So both lines are coincident

(iii)6x – 3y + 10       = 0
2x – y + 9            = 0
Compare the equation with

We get
a1 = 6,            b1       =- 3,               and c1 = 10
a2 =2              b2        =-1,                 and c2 = 9

Hence

So both lines are parallel

Question 2. On comparing the ratios a1/a2 , b1/b2 and c1/c2, find out whether the lines re