The number of integral values of m so

Question:

The number of integral values of $m$ so that the abscissa of point of intersection of lines $3 x+4 y=9$ and $y=m x+1$ is also an integer, is :

  1. (1) 1

  2. (2) 2

  3. (3) 3

  4. (4) 0


Correct Option: , 2

Solution:

$3 x+4 y=9$

$y=m x+1$

$\Rightarrow 3 x+4 m x+4=9$

$\Rightarrow(3+4 \mathrm{~m}) \mathrm{x}=5$

$\Rightarrow \mathrm{x}$ will be an integer when

$3+4 m=5,-5,1,-1$

$\Rightarrow \mathrm{m}=\frac{1}{2},-2,-\frac{1}{2},-1$

so, number of integral values of $m$ is 2

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