92 AlvGEBRA. 



Write system (a) so that it will read 



L-R=o (i) 



L-R=o (2) 



(c) 



(d) 

 L,-R„=o 



First, suppose T a known quantity. 



Then any set of values that will satisfy (c) must make L^— R,, 

 L^ — R^, . . . and L„— R„ each zero. But any set that makes 

 these zero must satisfy (d) also. Hence any solution of (c) is a 

 solution of (d). 



It is seen from (^3/ that any set of values that satisfies (d) must 

 makel^_ — Rj zero. Equation (^) will then become 



TrL-RJ=o. (s) 



Now since T is a known quantity, not zero, this cannot be sat- 

 isfied unless ly^— R^ is zero. Hence any set of values, in order to 

 satisfy (d), must make L^— R^ and L^— R, and also . . . Iv„ — R;, 

 each zero. But any set of values that makes these zero will satisfy 

 (c). Therefore any solution of (d) is a solution of (c). 



Now we have shown, Jirsi, that any set of values that will satisfy 

 (c) will satisfy (d), and second, that any set of values that will 

 satisfy (d) will satisfy (c). Hence the two systems are equivalent. 



Second, suppose T a function of some of the unknown quanti- 

 ties. 



In this case equation (^) may be satisfied by any set of values 

 that will satisfy the equation 



T=o 

 without assuming that L^—R^ is zero. Consequently f^j can be 

 satisfied without equation (2) being satisfied ; that is, without (c) 



