INDETERMINJtE PROBLEMS. 201 



X -j- — == my — max, and b = ■—-• Reducing the fxrft equa- 

 tion, bx-\-c =. viby — mabx, and y = —~f-~ . Again, redu- 

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



mabx+hx+c 



mb 



z=. mb—^ax, or mabx-^bx-j-c zz m'^¥ — mabx^ and 



therefore, x = '^„'Jt+b' ^^^ y — ^'^ — ^^ » therefore, y 



tn^ ab'' +mb'' +ac 



Zmab+b 



Suppose 9**+7«-f-i4 = /% and m :=: z ; then x =: 



4.49—14 , „ 4.1 47+2.4 04-42 o U ^ 1-1 



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



= 64 = (8)\ 

 Cor. I. Let (« = I, the expreflion becomes x^-^bx-j-c = ^' j 



fn>i> — c J m* b* +mb' •i'C ,_ 



^"^ * = 1^J+A . and;' = — J^^b • Thus, if x'-\-^x-i-/^ 



1 1 ^4—4 J 64+32+4 



= r, and w? = a ; then x = jg:;:^ = 3, and/ = ^^^^ =5; 



but 9+4.3+4 = 25 = (5)'' 



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

 comes (3V+^.v = J' ; and in this cafe, the formula; will be- 



come by reduaion, x = ~~^, and y -'^^^^ . Thus, if . 



9*'+i3* = y\ and m :=2; then ,v =7^;^ = 4, and/ = 4;.39.+a-ij 

 = 14; but9.i6+4.i3 = 196 = (i4)^ 



Vol. II. c c Case 



