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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?
Solve both eqns simply and take out (x,y) coordinates.put y = mx +1 in 3x + 4y – 9 = 0U 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 -6on solving m would satify asm = 0, -1 .simlarly do this for y coordinate.
given lines are3x+4y=9and y=mx+con solving both the equations , we get x=5/4m+3since =-coordinate is an integer,on solving these we get, m=-1,-2
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