EXTERN1INATION, in general, the ex tirpating ordestroying something. In alge bra, surds, fractions, and unknown quanti ties, are exterminated by rules for reduc ing equations. Thus to take away the frac tional form from these equations a=x ; y al x and — +b. i =—; both cases we multiply 2c the numerator of one fraction by the de nominator of the other, and the equations becomeay=bxand = 2 c x: so again, to take away the sign of the square, or cube, or other root, ast/a"--l-y" = 4; we raise the 4 z to the second'pow er, and take off the sign of the root on the other side of the equation thus, =16z= : and when n + 6 = x : then a b = xn. To exterminate a quantity from any equation there are divers rules.
See ALGEBRA.
We shall however give an instance in this place : thus to exterminate y out of these two equations b +y 3 subtract the upper equation from the der and there remains 3b.—a—x=2x-6, hence and — 3 Suppose also two equations given, in.
volving two unknown quantities, as a d x+e then shall y b Where the numerator is the difference of the products of the opposite coefficients, in the orders in which y is not found; and the denominator is the difference of the products of the oppoiite coefficients, taken from the orders that involve the unknown nuantities_ Pm; from the first equation it rears that ax=c—b and x = and from the second a equation, that d x = f — c y, and x = f-e fy . Therefore ; andcd—dby=af—aey, whence aey—dby=af—cd; and y a e To exemplify this theorem, suppose a= 5, b =7 „ c= 100, d e= 8, and f 5 X 80 — 3 X 1U0 80. 3= 100 5 ; d x 240 , 9 5 19 an 19 19' If three or four equations are given, in volving three or four unknown quantities, their values may be found much in the same manner.