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:
- 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 .
