A Treatise On Algebra, in Which the Principles of the Science Are Familiarly Explained ..
A Treatise On Algebra, in Which the Principles of the Science Are Familiarly Explained ..
Samuel Alsop
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= 45— 3 m -f ID n • ^ , 78 145 .^ 78 290 becomes 2^-^-^ar— -=-a?9=45-^-z- —^ or 14a? + 78 ar- 146 ar=ip 816 — 78 — 290, whence 63 ar s«s 53^ and a^rs^l. Digitized by VjOOQIC SIMPLE EQUATIONS. 115 In like manner y = 3 i^ = 4. Ex. 2. Qiven ax +by =c a'x + b'y^c'. Makiplying the latter by mr and adding to the formfir, w^ have ' . (a + maf) X + (^ + m*') y =» + «>«'• . If-now we assume 6 +m6' »? 6, or m = — rrf we have c-^tnc' h'e — he' * • a+T?Mi' ab'-^^a'i' and - y == -r; -= . p +6'y +c'3r = m' ...Ex. 3, Given s~cS5 '^^^ apd we will have fpr the sum of the equations (A), a'x+pd"x+ qaf'*x = m'+pm"+ qm"\ whencb - ^^ ra'+pm"-\^qm'^' in which the only difierence between the pumeratot and denominator is, that the former contains the absolute quan- tities m\ fn'*y and m"\ in place of the coefficients of a?, viz., c', a", and a'".
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