document.write( "Question 1184213: Find the number of integers values of m for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and mx - y = -1 is also an integer? \n" ); document.write( "

Algebra.Com's Answer #814782 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "We need solutions of the system of equations

\n" ); document.write( "3x+4y=9 [1]
\n" ); document.write( "mx-y=-1 ==> y=mx+1 [2]

\n" ); document.write( "in which m and x are both integers.

\n" ); document.write( "Substitute [2] into [1]:

\n" ); document.write( "3x+4(mx+1)=9
\n" ); document.write( "3x+4mx+4=9
\n" ); document.write( "(3+4m)x=5
\n" ); document.write( "x=5/(3+4m)

\n" ); document.write( "For x to be an integer, (3+4m) has to be a (positive or negative) factor of 5 -- 5, 1, -1, or -5.

\n" ); document.write( "3+4m=5
\n" ); document.write( "4m=2
\n" ); document.write( "m=1/2 not an integer

\n" ); document.write( "3+4m=1
\n" ); document.write( "4m=-2
\n" ); document.write( "m=-1/2 not an integer

\n" ); document.write( "3+4m=-1
\n" ); document.write( "4m=-4
\n" ); document.write( "m=-1 YES an integer
\n" ); document.write( "x=5/-1=-5

\n" ); document.write( "3+4m=-5
\n" ); document.write( "4m=-8
\n" ); document.write( "m=-2 YES an integer
\n" ); document.write( "x=5/-5=-1

\n" ); document.write( "ANSWER: Two integer values of m give solutions to the pair of equations in which x is also an integer.

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