Question

hey guys i have one doubt

how to find the integral values of a linear equation ax+by+c=0

that means (x,y) belongs to whole numbers

please help me its urgent
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Answer 1

Step-by-step explanation:

in order to find the integral solution of a linear equation..

first,

let us assume that a>b.

then,

divide the equation by b.

(ax+by+c)/b=0/b

=>a/b+y+c/b=0

then, express a=b*q+d where 0≤d<b

=>(b*q+d)x/b+c/b+y=0

=>qx+dx/b+c/b+y=0

now,assume that dx/b=integer =z

=>x=bz/d and y=-c/b-z(qb/d+1)

now take some examples...

5x+4y=200

=>(5x+4y)/4=200/4

=>x+x/4+y=50

=>so, x/4=integer =z

=>x=4z. thus,. y=50-5z

now, for z=1,2,3.... you'll always get integral values of x and y...

another example...

=>15x+2y=200

=>(15x+2y)/2=200/2

=>7x+x/2+y=100

x/2=z(integer)

=>x=2z. and thus y=100-15z

now,for z=1,2,3.... you'll always get integral values of x and y...

Answer 2

Answer:

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