106 OF ELIMINATION. [CHAP. VII. 



and it was observed that these equations, v being an indefinite 

 class symbol, were themselves equivalent. To prove this, it is 

 only necessary to eliminate from each the symbol v. The first 

 equation is 



y - v (1 - xz) = 0, 



whence, first making v = 1, and then v = 0, and multiplying the 

 results, we have 



(y- 1 +xz)y = 0, 



or yxz = 0. 



Now the second of the given equations becomes on transposition 



yx - v(l - z) = 0; 



whence (yx - 1 + z) yx = 0, 



or yxz = 0, 



as before. The reader will easily interpret the result, 



12. Ex. 3. As a subject for the general method of this 

 chapter, we will resume Mr. Senior's definition of wealth, viz. : 

 " Wealth consists of things transferable, limited in supply, and 

 either productive of pleasure or preventive of pain." We shall 

 consider this definition, agreeably to a former remark, as including 

 all things which possess at once both the qualities expressed in 

 the last part of the definition, upon which assumption we have, 

 as our representative equation, 



w = st {pr+p(l -r) + r(l - p)}, 

 or w = st{p + r(l -p)}, 



wherein 



w stands for wealth. 



s things limited in supply. 



t ,, things transferable. 



p things productive of pleasure. 



r things preventive of pain. 



From the above equation we can eliminate any symbols that 

 we do not desire to take into account, and express the result by 

 solution and development, according to any proposed arrange- 

 ment of subject and predicate. 



Let us first consider what the expression for w, wealth, would 



