**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 **