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

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.

(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

Infinity Learn · Accepted Answer

(i) x – $$3y$$ – $$3$$ $$=$$ $$0$$ and $$3x$$ – $$9y$$ – $$2$$ $$=$$ $$0a1a2=13$$, $$b1b2=-3-9=13$$,$$c1c2=-3-2=32$$ $$a1a2=b1b2$$≠$$c1c2Since$$, 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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