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Of the resolution of simple equations, containing two
- '3. -When there are two unknown quantities, and two independent simple equations involving them, they may be reduced to one, by *4;the three following rules :
Observe which of the unknown quantities is the least involved, and find its value in each of the equations, by the methods already explained ; then let the two values, thus found, be put equal to each other, and there will arise a new equation with only one unknown quantity in it, the value of which may be found as before. (b)
(b) This rule depends upon the well known axiom, that things which are equal to the same thing, are equal to each other ; and the two following methods are founded on principles which are equally simple and obvious.
Find the value of either of the unknown quantities in that equation in which it is the least involved ; then substitute this value in the place of its equal in the other equation, and there will arise a new equation with only one unknown quantity in it; the value of which may be found as before.
From the first equation, w=13-y; which value being substituted for 2, in the second, AGives 13-y-y=3, or 2y=13–3=10, -