Question

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method

3x – 5y = 20

6x – 10y = 40

Answer 1

3x – 5y = 20

6x – 10y = 40

`a_1/a_2 = 3/6 = 1/2`

`b_1/b_2 = (-5)/-10 = 1/2`

`c_1/c_2 = (-20)/-40 = 1/2`

`a_1/a_2 = b_1/b_2 = c_1/c_2`

Therefore, the given sets of lines will be overlapping each other i.e., the lines will be coincident to each other and thus, there are infinite solutions possible for these equations.