A problem by Arpita Karkera

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The number of integral values of m, for which the x-coordinate of the point of intersection of the lines 3x+4y=90 and y=mx+1 is also an integer is

3 0 1 2

Arpita Karkera by Arpita Karkera , 24, India

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1 solution

Given equations are : 3 x + 4 y = 90 a n d y = m x + 1 3x+4y=90 \ and \ y=mx+1

Now equating both equations w.r.t y we get, ( 3 + 4 m ) x = 86 (3+4m)x=86

Now taking integral factors of 86 which are,

( 1 , 86 ) , ( 2 , 43 ) , ( − 1 , − 86 ) a n d ( − 2 , − 43 ) (1,86), (2,43), (-1,-86) \ and \ (-2,-43)

On checking all the four cases we obtain that we only obtain integral values of both m as well as x only for the factors : ( 2 , 43 ) a n d ( − 1 , − 86 ) (2,43) \ and \ (-1,-86) for which values of m are 10 and -1 respectively.

Hence, number of integral values of m which give integral values of x are obtained is 2 \boxed{2}

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