Chapter 4.5, Problem 29MS

Here we celeb rate the power of algebra as a powerful way of finding unknown quarnities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

The Great R returns. The great rhombicuboctahedron (the Great R) from Mindscape 28 has lots of edges and vertices. Let E denote the number of edges and V denote the number of vertices. The values of E and V satisfy the equations $E+V=120\text{ and }5E-2V=264.$

Find the values of E and V.