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 and 3x – 9y – 2 = 0(ii) 2x + y = 5  and 3x + 2y = 8(iii) 3x – 5y = 20 and 6x – 10y = 40(iv) x – 3y – 7 = 0 and 3x – 3y – 15 = 0

# 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 and 3x – 9y – 2 = 0(ii) 2x + y = 5  and 3x + 2y = 8(iii) 3x – 5y = 20 and 6x – 10y = 40(iv) x – 3y – 7 = 0 and 3x – 3y – 15 = 0

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### Solution:

(i) x – 3y – 3 = 0 and 3x – 9y – 2 = 0

$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\ne \frac{{c}_{1}}{{c}_{2}}$

Since, the given set of lines are parallel to each other, they will not intersect each other. Hence, there is no solution for these equations.

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