document.write( "Question 1169727: how can you tell without graphing that there is one solution to the system... \n" ); document.write( "
Algebra.Com's Answer #794536 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "In Algebra,  there are  MANY  WAYS  to solve a system of linear equations and to determine if it has one or more solutions,\r
\n" ); document.write( "\n" ); document.write( "or does not have solutions at all.\r
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\n" ); document.write( "\n" ); document.write( "These methods are  Substitution,  Elimination,  the  Determinant method  (or  Cramer's rule).\r
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\n" ); document.write( "\n" ); document.write( "            The most general criterion for a linear system to have a unique solution is non-vanishing its determinant.\r
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\n" ); document.write( "\n" ); document.write( "            In simple terms,  if the determinant of the square coefficient matrix is not zero,  then the system has a unique solution .\r
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\n" ); document.write( "\n" ); document.write( "                    This general criterion has many modifications.\r
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\n" ); document.write( "\n" ); document.write( "            For example,  if a system with two equations in two unknown has  UNPROPORTIONAL  coefficient lines, then\r
\n" ); document.write( "\n" ); document.write( "            the determinant is non-zero and the system has a unique solution.\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Substitution method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns by the Elimination method \r
\n" ); document.write( "\n" ); document.write( "    - Solution of the linear system of two equations in two unknowns using determinant \r
\n" ); document.write( "\n" ); document.write( "    - Geometric interpretation of the linear system of two equations in two unknowns \r
\n" ); document.write( "\n" ); document.write( "in this site, and especially the last lesson in this list.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Systems of two linear equations in two unknowns\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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