...reduced to one which involves only one of the unknown quantities, by any of the following methods: 1" Method. In either equation, find the value of one...this value in the other equation, which will then only contain one nuknown quantity, whose value may be found by the rules before laid down. Trom the1...

...reduced to one which involves only one of the unknown quantities, by any of the following methods : 1st Method. In either equation find the value of one of...this value in the other equation, which will then only contain one unknown quantity, whose VOL. I. 2J Methad. Find an expression for one of the unknown...

...equation by 5, and the second by 2, and then, subtracting the second from the first. 2. By substitution. Find the value of one of the unknown quantities, in terms of the other and known quantities, in the more simple of the two equations ; and substitute this value instead of the quantity itself...

...20. Given 1+1=6, V'to ^ ;, , x , v { x and vand — |-i=5|, I Ans. **=:12,. andy=16. RULE II. 248. Find the value of one of the unknown quantities, in terms of the other and known quantities, in the more simple of the two equations ; and substitute this value instead of the quantity itself...

...equation by 5, and the second by 2, and then subtracting the second from the first. 2. By substitution. Find the value of one of the unknown quantities, in terms of the other and known quantities, in the more simple of the two equations ; and substitute this value instead of the quantity itself...

...Ex. 20. Given ^+^=6, 64 I to find the values o / , . x and y. and += Ans. a; =12, and #=16. KULE II. Find the value of one of the unknown quantities, in terms of the other and known quantities, in the more simple of the two equations ; and substitute this value instead of the quantity itself...

...Now, x - sy^~L?—™^H- 12 - « * •— g — g "~ 2 ~~ 86. METHOD 3d, In either equation, Jind a value of one of the unknown quantities, in terms of the other and known quantities ; substitute this value for the unknown quantity in the second equation, there will thence arise an...

...Indeterminate Analysis. CASE I. When the given equation contains two unknown quantities. RULE. 1 . Find the value of one of the unknown quantities in terms of the rest, as in step first, in the first example. _ 2. Divide the numerator by the denominator, if divisible,...

...the possible values of x and y in integer numbers, suppose the numbers a, b, c, prime to each other. Find the value of one of the unknown quantities in terms of the other. Thus, if the equation be by-lc ax—by=c, then z= — ; Or, ax+by=c, then x= — - — • Increase...

...each unknown quantity may be obtained by either of the three following methods. First Method. (54.) Find the value of one of the unknown quantities in terms of the other and the known quantities, from the first equation, by the method already given. Find the value of the same...