SIMPLE EQUATIONS. 



345 



much shorter methods for performing the operation, which 

 will be best learnt from practice. 



EXAMPLES. 



I. Given 



\ 



x-\r y + 2^=29 



^ I ^ » ^ k. to find;f,vanda, 



;^ y z 



l'^ 3 4 



From the first equation xrzip — -j— -z. 

 From the second x=:62 — 2y — 32. 



2y z 



From the third Xz=^2o . 



3 2 

 Whence 29 — y — 2:^62— 2jy' — 32, 



2y z 



And 29— V— ^zz=2o ; 



3 2 



But, from the first of these equations, )'Zz62''*— 2p— 2« 



3Z 

 And from the second yr227— — ; 



2 



QZ 



Therefore 33 — 22:=27 — — , or2r:i2. 



And ;;rr62— -29 — 2zzr62 — 29 — 24^9, 

 And Arz=29 — •;' — zz:29— 12 — 9==:8. 



i. Given 



-+^ + ^ = 



62 



~ -f- — -j ^^47 Yi to find A", ^ and z. 



X , y , z 



.7+7 + ^=33 



U u 



Fir;Jt, 



