\fdO'^ - Old Forge Coal Mines

124 ALGEBRA.
{d) {a' + xy = x' = Aa' + a*.
Performing the operation indicated in the first member, the
equation becomes
a' + 2aV -\-x' = x^-\- 4^" + a*.
Canceling x' (Art. 562) and transposing,
2«V = 4rt' + rt' — a\
Combining like terms, 2a^x = Aa'.
Dividing by 2^', ;r = 2. Ans.
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.r— 1 x-{-l _ 3
;r - 2 ;tr + 2 ~ ;r' - 4*
Clearing of fractions, the equation becomes
{x - 1) (;ir + 2) - (;ir + 1) {x - %) = 3.
Expanding, ;r' + ;r — 2 — ;ir' ;ir + + 2 = 3.
Uniting terms,
2;f = 3.
(234) ll;tr+3j=100. (1)
Ax-ly = 4.
(2)
Since the signs of the terms containing x in each equation
are alike, x may be eliminated by subtraction. If the first
equation be multiplied by 4, and the second by 11, the coefficients
in each case will become equal. Hence,
Multiplying (1) by 4, 44;r + 12j = 400. (3)
Multiplying (2) by 11, 44;r - = 77jF 44.
(4)
Subtracting (4) from (3), 89/ = 356.
^ = 4. Ans.
Substituting this value for jj/ in (2),
4.r - 28 = 4.
4;tr = 32.
;t- — 8. Ans.
(235) {a) /S = 243.
Extracting fifth root of both terms,
Cubing both terms, y = 'd^ = 27. Ans.
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