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Question
Write the integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer.
Solution
The given lines can be written as
mx \[-\] y + 1 = 0 ... (1)
3x + 4y \[-\] 9 = 0 ... (2)
Solving (1) and (2) by cross multiplication, we get:
\[\frac{x}{9 - 4} = \frac{y}{3 + 9m} = \frac{1}{4m + 3}\]
\[ \Rightarrow x = \frac{5}{4m + 3}, y = \frac{9m + 3}{4m + 3}\]
\[\text { For x to be integer we have, } 4m + 3 = 1, - 1, 5\text { and } - 5\]
\[ \Rightarrow m = \frac{- 1}{2}, - 1, \frac{1}{2} \text { and } - 2\]
Hence, the integral values of m are \[-\] 1 and \[-\] 2.
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