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3. Given }. *: *: to find the values of r
Here the analogy in the first, turned into an equation,
gives bac=ay, or w= #,
Let one or both of the given equations be multiplied, er divided, by such numbers, or quantities, as will make the term that contains one of the unknown quantities the same in each of them ; then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
2. Given #To to find the values of 3. and y. . Multiply the first equation by 2, and the second by 5 ; then 103–69–18, and 102-i-25 y=80. And if the former of these be subtracted from the lat
of the resolution of simple equations, containing three or more unknown quantities.
When there are three unknown quantities, and three independent simple equations containing them, they may be reduced to one, by the following method.
Find the values of one of the unknown quantities, in each of the three given equations, as if all the rest were known; then put the first of these values, equal to the second, and either the first or second equal to the third, and there will arise two new equations with only two unknown quantities in them, the values of which may be found as in the former case; and thence the value of the third. o or, multiply each of the equations by such numbers, or quantities, as will make one of their terms the same in them all ; then, having subtracted any two of these resulting equations from the third, or added them together, as the case may require, there will remain only two equations, which may be resolved by the former rules.
And in nearly the same way may four, five, &c. unknown quantities be exterminated from the same num:
ber of independent simple equations; but, in cases of this kind, there are frequently shorter and more commodious methods of operation, which can only be learnt from practice.
The usual method of resolving algebraical questions, is first to denote the quantities, that are to be found, by r, y, or some of the other final letters of the alphabet; then, having properly examined the state of the question, perform with these letters, and the known quantities, by means of the common signs, the same operations and reasonings, that it would be necessary to make if the quantities were known, and it was required to verify them, and the conclusion will give the result sought
Or, it is generally best, when it can be done, to denote only one of the unknown quantities by a or y, and then