Designing an adaptive optics (AO) system for extremely large telescopes (ELT's) will present new optical engineering challenges. Several of these challenges are addressed in this work, including first-order design of multi-conjugate adaptive optics (MCAO) systems, pyramid wavefront sensors (PWFS's), and laser guide star (LGS) spot elongation. MCAO systems need to be designed in consideration of various constraints, including deformable mirror size and correction height. The y,(bar y) method of first-order optical design is a graphical technique that uses a plot with marginal and chief ray heights as coordinates; the optical system is represented as a segmented line. This method is shown to be a powerful tool in designing MCAO systems. From these analyses, important conclusions about configurations are derived.