For real numbers $a , b , c , d , a ^ { \prime } , b ^ { \prime } , c ^ { \prime } , d ^ { \prime }$, consider the system of equations $$\begin{aligned}
a x ^ { 2 } + a y ^ { 2 } + b x + c y + d & = 0 \\
a ^ { \prime } x ^ { 2 } + a ^ { \prime } y ^ { 2 } + b ^ { \prime } x + c ^ { \prime } y + d ^ { \prime } & = 0
\end{aligned}$$ If $S$ denotes the set of all real solutions $( x , y )$ of the above system of equations, then the number of elements in $S$ can never be (A) 0. (B) 1. (C) 2. (D) 3.
For real numbers $a , b , c , d , a ^ { \prime } , b ^ { \prime } , c ^ { \prime } , d ^ { \prime }$, consider the system of equations
$$\begin{aligned}
a x ^ { 2 } + a y ^ { 2 } + b x + c y + d & = 0 \\
a ^ { \prime } x ^ { 2 } + a ^ { \prime } y ^ { 2 } + b ^ { \prime } x + c ^ { \prime } y + d ^ { \prime } & = 0
\end{aligned}$$
If $S$ denotes the set of all real solutions $( x , y )$ of the above system of equations, then the number of elements in $S$ can never be\\
(A) 0.\\
(B) 1.\\
(C) 2.\\
(D) 3.