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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 – 7 = 0

3x – 3y – 15 = 0

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#### Solution

x – 3y – 7 = 0

3x – 3y – 15= 0

`a_1/a_2 = 1/3`

`b_1/b_2 = (-3)/-3 = 1 `

`c_1/c_2 = (-7)/-15 = 7/15`

`a_1/a_2 ≠ b_1/b_2`

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations.

By cross-multiplication,

`x/(45-(21)) = y/(-21-(-15)) = 1/(-3-(-9))`

`x/24 = y/-6 = 1/6`

x/24 = 1/6 and y/-6 = 1/6

x = 4 and y = -1

∴ x = 4, y = -1.

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