If the lines $y - x = 5, 3 x + 4 y = 1$ and $y = m x + 3$ are concurrent then the value of m is

\frac{19}{5}

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1

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\frac{5}{19}

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none of these

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Solution

The correct option is C $\frac{5}{19}$
Given lines $y - x = 5, 3 x + 4 y = 1$ and $y = m x + 3$
For concurrency,
$∣ ∣ ∣ ∣ \begin{matrix} - 1 & 1 & 5 3 & 4 & 1 - m & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$
$\Rightarrow - 5 + 19 m = 0$
$\Rightarrow m = \frac{5}{19}$

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