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The number of integral values of \mathrm{m} for which the \mathrm{x}-coordinate of the point of intersection of the lines \mathrm{3 x+4 y=9 \: and \: y=m x+1} is also an integer, is
 

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

4


Answers (1)

Eliminate \mathrm{y} from the given equations, we obtain
\mathrm{ x=\frac{5}{3+4 m} }
As numerator of R.H.S. is 5 and \mathrm{ x } has to be an integer, then denominator

\mathrm{3+4 m=1,-1,5,-5 }

\mathrm{\Rightarrow 4 m=-2,-4,2,-8 }

\mathrm{\text { Or } m=-\frac{1}{2},-1, \frac{1}{2},-2}

Thus, two integral values of \mathrm{m=-1,-2} satisfy the condition.

Hence option 3 is correct.

Posted by

Sumit Saini

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