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Modulus of a Complex Number

The equations...

Question

The equations $3 x - 5 y + 2 = 0$ and $6 x + 4 = 10$ y have

A

an infinite number of solutions

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B

no solution

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C

two solutions

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D

a single solution

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Solution

The correct option is A an infinite number of solutions
$T h e g i v e n e q u a t i o n s a r e 3 x - 5 y + 2 = 0 - - - - (1) 6 x + 4 = 10 y - - - - (2) E q u a t i o n (1) c a n b e w r i t t e n a s y = \frac{3}{5} x + \frac{2}{5} - - - - (3) a n d e q u a t i o n (2) c a n b e w r i t t e n a s y = \frac{6}{10} x + \frac{4}{10} = \frac{3}{5} x + \frac{2}{5} - - - - (4) C l e a r l y f r o m (3) a n d (4) t h e s l o p e s a r e e q u a l a n d e a c h = \frac{3}{5} . S o t h e l i n e s n e v e r m e e t . ∴ T h e y h a v e i n f i n i t e s o l u t i o n s . (A n s)$

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Similar questions

Q. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions.
(i)

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

2 x + y = 5; 3 x + 2 y = 8

3 x - 5 y = 20; 6 x - 10 y = 40

x - 3 y - 7 = 0; 3 x - 3 y - 15 = 0

Q. The equations

3 x - 5 y + 2 = 0

6 x + 4 = 10 y

Q. The equation

3 x - 5 y + 2 = 0

6 x + 4 = 10 y

Q. Assertion :If the system of equations

2 x + 3 y = 7

2 a x + (a + b) y = 28

has infinitely many solutions, then

2 a - b = 0

Reason: The system of equations

3 x - 5 y = 9

6 x - 10 y = 8

has a unique solution.

Q. For what value of k, the pair of linear equations

3 x + k y = 9

6 x + 4 y = 18

give infinitely many solutions?

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