Question

Class X Board

Content Quality Required

Answer needed to be Explained Well

find those integral values of m for which the x co-ordinate of the point of intersection of lines represented by y=mx+c and 3x+4y=9 is an integer.

Answer 1

HEYA DEAR!!!!

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HERE IS YOUR ANSWER......

>> GIVEN :-

The two given lines are :- y = mx + 1 and 3x + 4y = 9

>> SOLUTION :-

Substituting the equation y = mx + 1 in equation 3x + 4y = 9,

=> 3x + 4(mx + 1) = 9

=> 3x + 4mx + 4 = 9

=> 3x + 4mx = 5

=> x(3 + 4m) = 5

=> x = 5/(3 + 4m)      ........(1)


>> NOW,

x can be integer in the following cases :-


> CASE 1 :-

IF,

=> 4m + 3 = 5

=> 4m = 2

=> m = 1/2


> CASE 2 :-

IF,

=> 4m + 3 = 1

=> 4m = -2

=> m = -1/2


> CASE 3 :-

IF,

=> 4m + 3 = -5

=> 4m = -8

=> m = -2


>> THEREFORE,

The integral value of m is -2 for which the x-coordinate of the point of intersection of lines is an integer.

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HOPE IT HELPS YOU DEAR,
THANK YOU ^_^  

Answer 2

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