Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1867 Excerpt: ... satisfied; if, for example, we take y = 1, we shall get z = 10-2 = 8; i(y = 2, x=6; ify = 3, x = 4; &c. One equation then between two unknown quantities admits of an infinite mimber of solutions; but if we have as many different equations, as there are quantities, the number of solutions will be limited. Thus, while each of the equations x = 10-2y, 4x + 4 = 3y, separately considered, is satisfied by an infinite number of pairs of values of x and y, there will only be found one pair common to both, viz. x = 2, y = 4, which are therefore the roots of the pair of equations,' x = 10-2y, and 4x + 4 = Zy. Equations of this kind, which are to be satisfied by the same pair or pairs of values of x and y, are called simultaneous equations. If there be three unknowns, there must be three equations, and so on: and moreover, these equations must all be different from one another; i. e. must all express different relations between the unknown quantities. Thus, if we had the equation x = 10-2y, it would be of no use to join with it the equation 2x = 20-4y (which is obtained by merely doubling it), or any other, derived, like this, immediately from the former; since this expresses no new relation between x and y, but repeats in another form the same as before. It may be observed, that if any two or more equations be given, any equations formed by adding or subtracting any multiples of these equations, will be also true, though expressing, in reality, no new relations between the quantities. Thus if x + Zy + 4z = 9, and 3x-2y + 17z = 25; then, subtracting the second from three times the first, we have 1ly-5z = 2. 95. There are generally given three methods for solving simultaneous equations of two unknowns; but the object aimed at is the same in each, viz. to cornbine ...
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