\fdO'^ - Old Forge Coal Mines

128 ALGEBRA.
(tx X
(r) am — b 7- H—— = 0, when cleared of fractions =
^ ' am
Transposing,
abm^ — b'^m — amx -|- ^jr = 0.
*
bx — amx = b*m — abm*.
Factoring, {b — am)x = bm{b — am) ;
bm(b — .
, am) ,
whence, x = — -rr r^ = bm. Ans.
{b — am)
(240) ;r+j = 13. (1)
xf = 36. (2)
Squaring (1) we have
;r» + 2xy+y = 169. (3)
Multiplying (2) by 4, 4,ry = 144. (4)
Subtracting (4) from (3),
x'-2xy-i-y = 25. (6)
Extracting the square root of (5),
x-y=±5. (6)
Adding (6) and (1),
Substituting the value of x in (1),
%r = 18 or 8,
,r = 9 or 4. Ans.
9+J' = 13,
or 4+7=13;
whence, 7=4,i ^^^
or z=
jf 9. i
(241) x'-y = 98. (1)
x-j = 2. (2)
From •
(2),
x = 2-\-j'. {3)
Substituting the value of x in (1),
8 + 12j + 6y +y -y = 98.
Combining and transposing,
ey + 12j = 90.
y -f 2^^ = 15.
^ + 2^^+ 1 = 15 + 1 = 16.
7+l=±4.
J = 3, or — 5. Ans.
Substituting the value of j in (3), x = 5, or — 3. Ans.