 The methods of solving integral equations depend upon principles which enable us to change a given equation into an equivalent equation whose solution is more easily obtained than that of the given one. This process is...  Elementary Algebra - Page 208by George Hervey Hallett, Robert Franklin Anderson - 1917 - 402 pagesFull view - About this book
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 714 pages
...equation. § 3. EQUIVALENT EQUATIONS. 1. Two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second is a solution of the first. Thus, the equations бж + 2 = 3о; + 6; 2ж + 2 = 6; ж + l = 3 are equivalent equations, since they... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1898 - 712 pages
...equation. § 3. EQUIVALENT EQUATIONS. 1. Two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second га a solution of tJie first. Thus, the equations 2. The methods of solving integral equations depend... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 512 pages
...called Equivalent Equations. In general, two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second is a solution of the first. 13. It is important to notice that the use of the principles given in Ch. I., Art. 17, may lead to... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 200 pages
...called Equivalent Equations. In general, two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second is a solution of the first. 13. It is important to notice that the use of the principles given in Ch. I., Art. 16, may lead to... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 664 pages
...are satisfied by the same root 9. 2. Two equations are equivalent when every solution of the ßrst is a solution of the second, and every solution of the second is a solution of the first. Eg, equations (1), (2), (3), and (4) of Art. 1. 3. The methods of solving integral equations depend... | |
 | George Egbert Fisher - 1901 - 622 pages
...called Equivalent Equations. In general, two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second is a solution of the first. 13. It is important to notice that the use of the principles given in Ch. I., Art. 17, may lead to... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 646 pages
...are satisfied by the same root 9. 2. Two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second i» a solution of the first. Eg, equations (1), (2), (3), and (4) of Art. 1. 3. The methods of solving... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1902 - 504 pages
...are satisfied by the same root 9. 2. Two equations are equivalent when every solution of the first is a solution of the second, and every solution of the second is a solution of the first. Eg, equations (1), (2), (3), and (4) of Art. 1. 3. The methods of solving integral equations depend... | |
 | Webster Wells - Algebra - 1904 - 642 pages
...unknown numbers which satisfies every equation of the system. 232. Two systems of equations, involving two or more unknown numbers, are said to be equivalent when every solution of either system is a solution of the other. PRINCIPLES USED IN SOLVING SIMULTANEOUS EQUATIONS 233. If... | |
 | Webster Wells - Algebra - 1906 - 550 pages
...ó , ••• is • — — • XXXVI. EQUIVALENT EQUATIONS 469. Two equations, each involving one or more unknown numbers, are said to be Equivalent when every solution of the first is a solution of the second, and every solution of the second a solution of the first. 470. To solve... | |
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