Question

let c be a natural number such that \(2\leq c\leq 8\). If simultaneous equations
\(2x-1+cy=0\)
\(x^2+2xy-y=0\)
in x,y has a pair of rational solution, what are c,x,y?

Answer 1

any idea?

Answer 2

for the second equation, to me , i rewrite as x^2 +y(2x-1)=0 or \(y=-\dfrac{x^2}{2x-1}\)

Answer 3

plug to the first one to solve for x, consider the condition of 2<c<8 , you may have an outlet.

Answer 4

Thanks!!