For which values of a and b does the following pair of linear equations have an infinite number of solutions?  2x-3y=7 and ax+3y=b

# For which values of a and b does the following pair of linear equations have an infinite number of solutions?  2x-3y=7 and ax+3y=b

1. A
2. B
3. C
4. D

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### Solution:

Given that the pair of linear equations are   and  .
A system of linear equations will have infinite solutions when    satisfies.
Here, and .

As the given linear equations have an infinite number of solutions, so,
$\frac{2}{a}=\frac{-3}{3}=\frac{-7}{-b}$
Taking the first two fractions,

Taking the last two fractions,
$⇒\frac{{-}{3}}{{3}}{=}\frac{{-}{7}}{{-}{b}}$

Therefore, values of a and b are -2 and -7 respectively.
Hence, option (1) is correct.

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