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Inconsistent Pair of Linear Equations

Which of the ...

Question

Which of the following pairs of equations represent inconsistent system?

3 x - 2 y = 8

2 x + 3 y = 1

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3 x - y = - 8

3 x - y = 24

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x - y = m

x + m y = 1

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5 x - y = 10

10 x - 6 y = 20

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Solution

The correct option is B $3 x - y = - 8$
$3 x - y = 24$
For a pair of linear equations to be inconsistent, the equations must satisfy the given condition which is
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Since, the equations $3 x - y = - 8$ and $3 x - y = 24$ clearly satisfy the above condition $\frac{3}{3} = \frac{- 1}{- 1} \neq \frac{- 8}{24}$ , the pair of equations represents inconsistent system.
In options A, C and D, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

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