## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

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Page 87

... found , which is generally in terms of the other unknown quanti- ties , in all the other equations in which it occurs . Solution of Equations .

... found , which is generally in terms of the other unknown quanti- ties , in all the other equations in which it occurs . Solution of Equations .

**Elimination**by Substitution . The new CH . III . IV . ] EQUATIONS OF THe first degree . 87. Page 88

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Solution of Equations .

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Solution of Equations .

**Elimination**by ...**eliminations**be still far- ther reduced in number and in the number of their unknown quantities , until only one ... Page 91

... two equations 7 + x 5 5y - 7 2 2x - y 3y - 5 , 4 4x - 3 + 18 – 5 1 . 6 Ans . x = 3 . 3 , y = 2 = 2 . Equations of the First Degree solved by

... two equations 7 + x 5 5y - 7 2 2x - y 3y - 5 , 4 4x - 3 + 18 – 5 1 . 6 Ans . x = 3 . 3 , y = 2 = 2 . Equations of the First Degree solved by

**Elimination**by Substitution CH . III . IV . ] EQUATIONS of the first degree . 91. Page 92

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**Elimination**by Substitution . 4. Solve the two equations ax = by , x + y = c . b c ac Ans . x = a + b ' y = a + b 5. A says to B , " give me $ 100 , and I shall have as 66 much as you . " No , " says B to A , " give me rather $ 100 ... Page 93

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**Elimination**by Substitution . a ' , and the second by b ' , the product of these sums exceeds the products of the two numbers themselves by c ' . a'c - ac'aa'b ' — a a ' b Ans . The first is a'b - ab ' is the second bc - b'cabb ' — a ...### Other editions - View all

### Common terms and phrases

126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence