Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution,

(i) x − 3y – 3 = 0

3x − 9y – 2 = 0

Comparing equation x − 3y – 3 = 0 with a1x +b1y + c1 = 0 and 3x − 9y – 2 = 0 with a2x +b2y + c2 = 0,

We get,

Therefore, the given sets of lines are parallel to each other. Therefore, they will not intersect each other and thus, there will not be any solution for these equations.

2x + y = 5

3x + 2y = 8

Comparing equation 2x + y -5= 0 with a1x +b1y + c1 = 0 and 3x + 2y -8= 0 with a2x +b2y + c2 = 0,

We get,

Herethis means that there is unique solution for the given equations.

By cross-multiplication method,

3x − 5y = 20

6x − 10y = 40

Comparing equation 3x − 5y = 20 with a1x +b1y + c1 = 0 and 6x − 10y = 40 with a2x +b2y + c2 = 0 ,

We get

It means lines coincide with each other.

Hence, there are infinite many solutions.

(iv) x − 3y – 7 = 0

3x − 3y – 15 = 0

Comparing equation x − 3y – 7 = 0 with a1x +b1y + c1 = 0 and 3x − 3y – 15 = 0 with a2x +b2y + c2 = 0,

We get,

Here this means that we have unique solution for these equations.

By cross-multiplication,