Straight Line and Pair of Straight Lines 1 Question 27

27. The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3 x+4 y=9$ and $y=m x+1$ is also an integer, is (2001,1M)

(a) 2

(b) 0

(c) 4

(d) 1

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Solution:

  1. On solving equations $3 x+4 y=9$ and $y=m x+1$, we get

$$ x=\frac{5}{3+4 m} $$

Now, for $x$ to be an integer,

$$ 3+4 m= \pm 5 \text { or } \pm 1 $$

The integral values of $m$ satisfying these conditions are -2 and -1 .



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