Question

Find Four Solutions of -2x +3y=7
plz give the answer fast and correct​

Answer 1

Answer:

What are the four solutions for the following equation :- 2x + 3y = 7?

Although the eqn has infinitely many real solutions but I am restricting to only integral solutions.

Since, (x,y)=1 thus, by Bezout's theorem integral solutions are possible for this linear Diophantine eqn.

Then,

2x+3y= 7(3–2)=> 2(x+7)= 3(7-y)

=> x+7= 21−3y2=3(7−y)2

Now let 7−y=2λ

So, y=7−2λ and x=3λ−7

Now, let us further restrict ourselves to only positive integral solutions of x and y.

Then,

Only possible value of \lambda = 3

Then, values of (x,y)= (2,1)

Other values (integral) you can calculate by putting λ = several integers like 0,1,2,3,-1,etc.

I have modified the question to make it more interesting