MathematicsAre the following pair of linear equations consistent? -3x-4y=12 and 4y+3x=12.

Are the following pair of linear equations consistent?

$- 3 x - 4 y = 12$ and $4 y + 3 x = 12$ .

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A
No
B
Yes
C
Data Insufficient
D
None of these

Solution:

The given pair of linear equations can be written as,

- 3 x - 4 y - 12 = 0

and

3 x + 4 y - 12 = 0

.
Here

a_{1} = - 3, b_{1} = - 4, c_{1} = - 12

,
and

a_{2} = 3, b_{2} = 4, c_{2} = - 12

∴ \frac{a_{1}}{a_{2}} = \frac{- 3}{3}

= - 1

\frac{b_{1}}{b_{2}} = \frac{- 4}{4}

= - 1

\frac{c_{1}}{c_{2}} = \frac{- 12}{- 12}

= 1

\Rightarrow \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

Therefore, the given pair of linear equations is inconsistent.
Hence, the correct option is 1.

Are the following pair of linear equations consistent?

$- 3 x - 4 y = 12$ and $4 y + 3 x = 12$ .

Solution:

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