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Question

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

A
2
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B
4
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C
1
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Solution

The correct option is A 2
Solving given lines for the x-coordinate of the point of intersection
3x+4(mx+1)= 9
or (3+4m)x=5 or x=53+4m
For x to be an integer, 3+4m should be a divisor of 5, i.e., 1,1,5,or5. Hence,
3+4m=1 or m=12(not an integer)3+4m=1 or m=1(integer)3+4m=5 or m=12(not an integer)3+4m=5 or m=2(integer)
Hence, there are two integral values of m.

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