ALGEBRA. 



the unknown quantity, and the value re- 

 quired is obtained. 



\:\ 1. To find the value of or in the 

 equation ,>j~ 5=2.3 

 l>y trans]> 



or 4o-=2S 



, ,. . . 28 _ 



by division -r= =7- 



J Let J-f f |=4r 17. 



2x 



Mult, by 2, and 2 .r + x =8x 34 



Si 



Mult by 3, and 6 .r-f 3.r 2.i;=24a- iu2 

 ".p. 6 .1 -f 3 J- 2 x 24 x= 102 

 or 17 j- = 10-2 

 17x=102 



102 .. 

 ,= =6. 



- + -=r. 

 a x 



,6 a 

 '+ = cr ' 



.r-j-A =r a-i' 

 .r c </.(= 6 </ 

 or r . .=/; 



value may be found by the rules before 

 laid down. 



From the first equal. x=10 u ; hence, 

 2x=20 2y, 



by subst.20 2y 3y=5 



2U 5=r-- 



15=5. v 



hence also, x=10 y=10 3=7. 



2d Method Find an expression for one 

 of the unknown quantities in each . qua- 

 tion ; put these expressions equal to each 

 other, and from the resulting equation the 

 other unknown quantity may be found, 



Let 



From the first equat. x=a y 



from the second, b x=.de c y, and r 

 _ tie cy 

 b 





fore y= 



- 

 F.x.4.5 -- -= 



b a 6y=de cy 

 < I' by=de ba. 

 c b .y=.df I) a 

 debn 



55 x 4=11 



55 4-1-33 = 

 ^ 



o, x=a y ; thai 

 </' b a ca ba d e -f- b 

 t^u - =- - 

 c A 



c a de 

 cb 



r b 



6 x+9 x-j-4 x=72 -r-S-r-15 

 19 x=95 



95 

 x=-=5. 



If thcrr be two independent simple 

 equations involving two unknown quanti- 

 ties they may be ivdured to one which 

 involves only one of the unknown quan- 

 tities, by any ofthc following methods: 



Ut 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, \v hi' h will then 

 only contain one n- 



VOL I 



3d Method. Ifeitlierof the unknown 

 quantities have the same co-efficient in 

 both equations, it may be exterminated by 

 subtracting, or adding, the equati. 

 cording as the sign of the unkno\\ n quan 

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

 ferent. 



To find x and y. 



Hy subtraction, 2 t/=8, and ^^4 

 By addition, 2 x 22, and x- 11 



If the co-efficients of the unknown 

 quantity to be exterminated be different, 

 multiply the terms ot' the first equa- 

 tion by the co-efficient of the unknown 

 quantity 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 1 equa- 

 tions, . -ase. 



