Q73 / 200 · Manipal (MET) 2013 · Mathematics

The number of rational values of $m$ for which the $y$-coordinate of the point of intersection of the lines $3 x+2 y=10$ and $a=m y+2$ is an integer is

  • A
    $2$
  • B
    $4$
  • Correct answer
    C
    $6$
  • D
    $8$

Solution

From the given equation, $3(m y+2)+2 y=0$ $\Rightarrow \quad y(3 m+2)=4$ $\Rightarrow \quad y=\frac{4}{3 m+2}$, since, $y \in l \Rightarrow 3 m+2$ $\Rightarrow \quad \pm 1, \pm 2, \pm 4$ $\Rightarrow m=-1,-\frac{1}{3},-\frac{4}{3}, 0, \frac{2}{3},-2$

Hence, the correct answer is option: 'C'.

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