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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?
Answer by greenestamps(13214)   (Show Source):
You can put this solution on YOUR website!
We need solutions of the system of equations
3x+4y=9 [1]
mx-y=-1 ==> y=mx+1 [2]
in which m and x are both integers.
Substitute [2] into [1]:
3x+4(mx+1)=9
3x+4mx+4=9
(3+4m)x=5
x=5/(3+4m)
For x to be an integer, (3+4m) has to be a (positive or negative) factor of 5 -- 5, 1, -1, or -5.
3+4m=5
4m=2
m=1/2 not an integer
3+4m=1
4m=-2
m=-1/2 not an integer
3+4m=-1
4m=-4
m=-1 YES an integer
x=5/-1=-5
3+4m=-5
4m=-8
m=-2 YES an integer
x=5/-5=-1
ANSWER: Two integer values of m give solutions to the pair of equations in which x is also an integer.
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