 Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the...  Elementary Algebra - Page 213by Henry Sinclair Hall, Samuel Ratcliffe Knight - 1895 - 478 pagesFull view - About this book
 | Stephen Chase - Algebra - 1849 - 348 pages
...indeterminate. By like reasoning, we shall find, that any number whatever of equations must be indeterminate, if the number of unknown quantities is greater than the number of INDEPENDENT equations. NOTE«. (1). Independent equations are those, of which no one is implied by the rest. Thus arh/ = 3,and... | |
 | Joseph Ray - Algebra - 1852 - 366 pages
...Z—lJa'—4=APPENDIX. INDETERMINATE ANALYSIS. ART. 1. Indeterminate Analysis is the resolution of equa(ions where the number of unknown quantities is greater than the number of independent equations, and where the results are required in positive integers. It is shown (Alg. Part II. Art. 168,) that... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1891 - 606 pages
...positive integers ; and with this restriction, as we shall see later, the number of solutions is limited. If the number of unknown quantities is greater than...an unlimited number of solutions, and the equations are said to be indeterminate. In the present section we shall only discuss the simplest kinds of indeterminate... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 552 pages
...a)2 + c(o - b)2 + 8 aie. CHAPTER XXXI. INDETERMINATE EQUATIONS OF THE FIRST DEGREE. 321. lu. Art. 167 we saw that if the number of unknown quantities is...us to express the solutions in a very simple form. Ex. 1. Solve 7 x + 12 y = 220 in positive integers. Transpose and divide by the smaller coefficient... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1897 - 548 pages
...+ 8 обе. CHAPTER XXXI. INDETERMINATE EQUATIONS OK THE FIRST DEGREE. 321. In Art. 167 we валу that if the number of unknown quantities is greater...however, we can limit the number of solutions. When positif? integral values of the unknown quantities are required, the equations are called simple indeterminate... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...PROBLEMS* INDETERMINATE EQUATIONS OF THE FIRST DEGREE 252. It has already been learned that, in case the number of unknown quantities is greater than the...will be an unlimited number of solutions, and the equation will be indeterminate. However, it is possible to limit the number of solutions by introducing... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...PROBLEMS* IN-DETERMINATE EQUATIONS OF THE FIRST DEGREE 252. It has already been learned that, in case the number of unknown quantities is greater than the...will be an unlimited number of solutions, and the equation will be indeterminate. However, it is possible to limit the number of solutions by introducing... | |
 | Arthur Schultze - Algebra - 1905 - 674 pages
...+ 2y = 7, has an infinite number of solutions. Similarly any system of equations is indeterminate, if the number of unknown quantities is greater than the number of equations. By introducing the condition that the roots shall be positive integers, the number of solutions... | |
 | Arthur Schultze - Algebra - 1906 - 584 pages
...+ 2 y = 7, has an infinite number of solutions. Similarly any system of equations is indeterminate, if the number of unknown quantities is greater than the number of equations. By introducing the condition that the roots shall be positive integers, the number of solutions... | |
 | Henry Sinclair Hall - 1918 - 382 pages
...a(bc)a + b(ca)2 + c(ab CHAPTER XXXI. INDETERMINATE EQUATIONS OF THE FIRST DEGREE. 321. In Art. 167 we saw that if the number of unknown quantities is...us to express the solutions in a very simple form. Ex. 1. Solve 7 ж + 12 y = 220 in positive integers. Transpose and divide by the smaller coefficient... | |
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