Ex. 2. Let * -(*•- - 
Mult, by 2, and 2 x -{- x 
Mult, by 3, and 6 x -j- 3 ,r ■ 
by transp. 6 x 3 x — 
or — 1 7 x = ■ 
17 x = 102 
102 
17 
4 x - 
ALGEBRA 
- 17. 
2 x 
= 8 x — 34 
i t — 2 x — 24 x — 102 
• 2 a.’ — 24 x = — 102 
— 102 
_ „ 1 . h 
Ex. 3. *■ -1— - — c. 
a x 
, ba 
i H — = c 
x b a = c 
x — cax — 
or cax - — ■ x — 
■bd 
j.e. ca- 
1 . x . 
ba 
: b a 
~ b a 
Ex. 4. 5 
: x — 3. 
c a •— 1 
x -}- 4 
~ir 
55 — x — 4= 11a— 33. 
55 — 4 -j- 33 = 11.x -(- x 
84 = 12* 
84 ~ 
a ' = T2 = 7 - 
Ex. 5. x -)■ 
Sr — 5 
= 12 - 
2* — 4 
4 .r — 8 
2 
2x-|-3x— 5 =24- 
1 • i> 
6ar-)-9* — 15 = 72 — 4 x 8 
6x-f-9r-J-4x = 72-j-8-j-15 
19 x = 95 
95 e 
x = - = 5. 
2 d Method. Find an expression for one of 
the unknown quantities, in each equation; 
put these expressions equal to each other, anil 
from the resulting equation the other un- 
known quantity may be found. 
Let 
:ffl l 
/ — de S 
*+y 
bx-\-cy 
From the first equat. * = a - 
from the second, bx = de 
d e c y • 
To find x and y. 
y 
-cy-, 
and x : 
therefore a — y — 
de — ( 
ba — by z=de — cy 
cy — by = de — ba 
■ b a 
■ b.y — de ■ 
de — bn 
Also, x — a 
de — ba 
c — b 
— de 
c — b 
y ; that is, 
c a — b a — de -j- J a 
3 d Method. If either of the unknown quan- 
tities have the same co-efficient in both equa- 
tions, it may be exterminated by subtracting, 
or adding, the equations, according qs the 
sign of the unknown quantity, in the two 
cases, is the same or different. 
Let 
| x f rf j To find x and y. 
By subtraction, 2 y = 8, and y = 4 
By addition, 2 x = 22, and x = 11. 
If there be two independent simple equa- 
tions involving two unknown quantities, they 
maybe reduced to one which involves only 
one of the unknown quantities, by any of the 
following methods : 
1 st Method. In either equation, find the 
value of one of the unknown quantities in 
terms of the other and known quantities, and 
for it substitute this value in the other equa- 
tion, which will then only contain one un- 
known quantity, whose value may be found 
by the ruies .before laid down. 
l£t j 2 t-lfyL 5 S T ° find X and V- 
From the first equat. x = 10 — y ; hence, 2 x 
= 20 — 2 y, 
by subst. 20 — 2 y — 3 y = 5 
20 — 5 = 2 y -f- 3 y 
15 = 5y 
hence also, * = 10 — y = 10 — 3 = 7. 
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 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 result- 
ing equations, as in the former case. 
Ex. 1. Let \ '^ T . ^ l To find* and y. 
(2x-|-7y = 81$ •' 
Multiply the terms of the first equation by 2, 
and the terms of the other by 3, 
then 6 x — 1 0 y — 26 
6 x -|- 2 1 y = 243 
By subtraction, — 31 y = — (217 
, 2!7 
and y — — — 7 ; 
also, 3 ,r — 5 y = 13, or 3 x — 35 = 1 Hr 
therefore, 3 x = 13-j-35 = 48 
a 48 
, and x = — = 16. 
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