1957 AHSME Problem 34

The points that satisfy the system x + y = 1,\, x^2 + y^2 < 25, constitute the following set:

\begin{array}{l} \textbf{(A)}\ \text{only two points} \qquad \\ \textbf{(B)}\ \text{an arc of a circle}\qquad \\ \textbf{(C)}\ \text{a straight line segment not including the end-points}\qquad\\ \textbf{(D)}\ \text{a straight line segment including the end-points}\qquad\\ \textbf{(E)}\ \text{a single point} \end{array}

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