New Elementary Algebra, Embracing the First Principles of the Science
New Elementary Algebra, Embracing the First Principles of the Science
Charles Davies
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A; = 10, y = 20. 116 Having explained the principal methods of elimina- tion, wo shall add a feAv examples which may be solved by any one of them ; and often indeed, it may be advantageous to emj)loy them all, even in the same example. GENERAL EXAMPLES. Find the values of x and y in the following simultaneous equations : 1. 2a; 4- 3y = 16, and 3a; — 2y = 11. Ans. A; = 5, y =• 2. ELIMINATION, 1« 2, L _ii = _- and ■ — ~ z=. — ft ^ 4 20* 4^5 120 A 1 1 3. ? + 7y = 99, and ^ + 1x = 51. Ans. 25 == 7,... y = 14 4. 1-12=1 + 8. ^l + l-S = 'l^ + . 1. 6. 4o* * - ly + y = C} uln«. A; = 60, y = 40. A; = 6. --- + 7. = 41 ia; - 2^ + 4iy = 12} j 5 3y»~ g, 2a; - y 6 "^ 4 6a;-y + ?-^ = ^^^ j '3a; - 8 y — 6 Ans. Ans. Ans, + "—T- + y = 18 TT 8.^ 9. 8a - 3 — 6 - y 79 4j; — 4 V — 5 ix-iy + V-* Ans. Ans. y = 8 a; = 6. y = s. a; = 9. y=8. X = 10. y= 12 x=:e. y = 5. \/ / 142 10. ELEMENTARY ALGEIJllA. c -\- ab — bd X = A71S. ax — by = c a — y -^r X = d a — b y z= a^ + c — ad a — b J J j IS-T + Ty- 341 :=.
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