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the no of integral values of m for which x coordinate of point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer is?

the no of integral values of m for which x coordinate of point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer is?

Grade:11

3 Answers

Vikas TU
14149 Points
7 years ago
Solve both eqns simply and take out (x,y) coordinates.
put y = mx +1 in 3x + 4y – 9 = 0
U would get,
3x + 4(mx + 1) – 9 = 0
(3 + 4m)x = 6 
x = > 6/(3 + 4m)
and y = 6m/(3+4m) + 1 = > (7m +3)/(3+4m)
Now for x to be integer,
the modulus of denominator value should not be greater equals than 6.
Therefore,
(3+4m) less than equal to 6 and greater than -6
on solving m would satify as
m = 0, -1 .
simlarly do this for y coordinate.
Vaishnavi Malladi
13 Points
5 years ago
given lines are
3x+4y=9
and y=mx+c
on solving both the equations , we get 
x=5/4m+3
since =-coordinate is an integer,
on solving these we get, m=-1,-2
ankit singh
askIITians Faculty 614 Points
3 years ago
and 3x + 4y = 9 ------------ (2) is the solution set of the equations. Therefore, integral value of m is -2 for which the x-coordinate of the point of intersection of lines is an integer.Dec 31, 2018

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