Question 1184213
<br>
We need solutions of the system of equations<br>
3x+4y=9 [1]
mx-y=-1  ==>  y=mx+1 [2]<br>
in which m and x are both integers.<br>
Substitute [2] into [1]:<br>
3x+4(mx+1)=9
3x+4mx+4=9
(3+4m)x=5
x=5/(3+4m)<br>
For x to be an integer, (3+4m) has to be a (positive or negative) factor of 5 -- 5, 1, -1, or -5.<br>
3+4m=5
4m=2
m=1/2 not an integer<br>
3+4m=1
4m=-2
m=-1/2 not an integer<br>
3+4m=-1
4m=-4
m=-1  YES an integer
x=5/-1=-5<br>
3+4m=-5
4m=-8
m=-2  YES an integer
x=5/-5=-1<br>
ANSWER: Two integer values of m give solutions to the pair of equations in which x is also an integer.<br>