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Equation of line in Straight lines

Question

The number of integer value 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

Moderate
Solution

x-coordinate of the point of intersection is given by

3x+4(mx+1)=9x=53+4m

As x is an integer, 3+4m must be a divisor of 5

so, 3+4m=±1 or ±5m=1 or 2

(considering the integer value only)



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