ALGEBRA. 



the unknown quantity, and the value re- 

 quired is obtained. 



Ex. 1. To find the value of 07 in the 

 equation 3o7 5=23 07. 



by transp. 3x+.r=23+5 

 or 4o7=28 



28 _ 

 by division 07= =o. 



Ex. 2. Let o7+| |=4.r 17. = 1 =3 



Mult, by 2, and 2 07 + 07 ^= 8 07 34 hence also, 07=10 1/=10 3=7. 



value may be found by the rules before 

 laid down. 



T find * and 



From the first equal. 07= 10 y\ hence, 

 2 07=202 y, 



by subst. 202 y 3 y 

 20 5 

 16=5 # 



Mult, by 3, and 6 x+3 x 2 xx=24 a: 102 

 by transp. 6 x+3 x2 x 24 x= 102 

 or 17 x = 102. 

 17o-=102 



102 . 



Ex. 3.i 

 a 



x 



07+6 a=c a x 

 x c a x b d 

 or c a x 07= b a 



i. e. c a 1. 07=6 a 

 b a 



Ex. 4. 



x -3. 



^ 



55 07 4=11 a: 33. 

 55 4-f- 33 = 11 x-{-x 

 84=12 x 



2 07+3 075= 



6 07+9 0715=72 4 07+8 

 6 07+9 07+4 07=72 +8+15 

 19 07=95 



_95 



~19~ 



If there be two independent simple 

 equations involving two unknown quanti- 

 ties, they may be reduced to one which 

 involves only one of the unknown quan- 

 tities, by any of the following methods : 



1st Method. In either equation find 

 the value of one of the unknown quanti- 

 ties in terms of the other and known 

 quantities, and for it substitute this value 

 in the other equation, which will then 

 only contain one unknown quantitv, whose 



VOL. I. 



2d Method. Find an expression for one 

 of the unknown quantities in each equa- 

 tion ; put these expressions equal to each 

 other, and from the resulting equation the 

 other unknown quantity may be found. 



From the first equat. 07=0 y 



from the second, b x=d e c y, and 



_ de cy 



~ b 



f d e c y 



therefore a y= - - - 



b 



b a b y=d e c y 

 c y b y=zd e b a 

 c b . yd e b a 

 d e b n 



Also, x=a y ; that is, 

 de ba ca ba de-\-ba 



c b c b 



_ c a d e 

 '' cb ' 



3d Method. If either of the unknown 

 quantities have the same co-efficient in 

 both equations, it may be exterminated by 

 subtracting, or adding, the equations, ac- 

 cording as the sign of the unknown quan- 

 tity, in the two cases, is the same or dif- 

 ferent. 



To find 07 and r/. 



Let 



By subtraction, 2 #=8, and y=4 



By addition, 2 o?=22, and 07= 11. 



If the co-efficients of the unknown 

 quantity to be exterminated be different, 

 multiply the terms of the first equation 

 by the co-efficient of the unknown quan- 

 tity in the second, and the terms of the 

 second equation by the co-efficient of the 

 same unknown quantity in the first ; then 

 add, or subtract, the resulting equations, 

 as in the former case. 





