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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 - 3 = 0 3x - 9y -2 - 0

Q1.    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.

                (i)    \\x - 3y -3 = 0\\ 3x - 9y -2 = 0

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Given, two equations,

\\x - 3y -3 = 0.........(1)\\ 3x - 9y -2 = 0........(2)

Comparing these equations with a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0, we get

\frac{a_1}{a_2}=\frac{1}{3}

\frac{b_1}{b_2}=\frac{-3}{-9}=\frac{1}{3}

\frac{c_1}{c_2}=\frac{-3}{-2}=\frac{3}{2}

As we can see, 

\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}

Hence, the pair of equations has no solution.

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