The number of solutions `(x, y)` where x and y are integers, satisfying `2x^2 + 3y^2 + 2x + 3y = 10` is

The number of solutions of 2^(2x)-3^(2y)=55, in which x and y are integers,is

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4) and y=2xy is

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x le y .

The number of ordered pairs of integers (x,y) satisfying the equation x ^2+6x+y^2 =4 is

If (x-1)^2+(y-2)^2=0 , where x and y are integers, then the value of 2x+3y is :