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
