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

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

(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

(ii)            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