INDETERMINJTE PROBLEMS, 201 



x + — = my — max, and b zz ■■■■. Reducing the firft equa- 



. v , , y f . mabx+bx+c J , 



tion, bx-\-c zz mby—mabx, and y zz — — ^ ^ — - , Again, redu- 

 cing the fecond, mb zz y-\-ax, and y zz mb—axj confequently, 



mabx+bx-{-c r - r i r j i t 



" T~~~~° ~ z — ax * or ma bx-\-bx-\-c zz m^o z -—mabx i and 



m % b % — c 



therefore, x zz "j mabJs . b • But y zz mh—ax. ; therefore, y zz 



m % ab % *\-mb % -\-ac 

 2?nab-\-b 



Suppose gx^jx+iq, zz y% and m zz 2 \ then .v ~ 



4.49—14 , 4,147+2.49+42 . . , M . 



-^^y~ - 2, and y = -—^7^-— = 8 ; but 9.4+7.2+14 



= 64 = (8)\ 



Cor. 1. Let a zz 1, the expreflion becomes #*+&*+<? =- ^» • 



m*b % ~~c m*b*+mb 9 +c ,_. ,~ 



and « = "7^j, and j = - - 2mb+b . Thus, if ff'+4*+4 



= y% and *i = 3 ; then * = 7^ = 3, and;/ = m - • = 5} 



but 9+4.3+4 = 25 = (5) s - 



Cbr. 2. When the third term is wanting, the expreffion be- 

 comes (Px*+bx zz y % ; and in this cafe, the formulas will be- 



come by reduction, • = ££„ &ndy ~2^t. Thus, if . 



9**+i3* = y\ and mzz2\ then x zz 7™- zz 4, andj = ±i2±±l3 

 = 145 0^9.16+4.13 = 196 = (14)*. 



Vol. II. c c Case 



