1955 AHSME Problem 43

The pairs of values of x and y that are the common solutions of the equations y=(x+1)^2 and xy+y=1 are:

\begin{array}{l} \textbf{(A)}\ \text{3 real pairs}\qquad\textbf{(B)}\ \text{4 real pairs}\qquad\textbf{(C)}\ \text{4 imaginary pairs}\\ \textbf{(D)}\ \text{2 real and 2 imaginary pairs}\qquad\textbf{(E)}\ \text{1 real and 2 imaginary pairs} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.