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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
x – 3y – 3 = 0
3x – 9y – 2 = 0
Solution
x – 3y – 3 = 0
3x – 9y – 2 =0
`a_1/a_2 = 1/3`
`b_1/b_2 = (-3)/-9 = 1/3 ` and `c_1/c_2 = (-3)/-2 = 3/2`
`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`
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.
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