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)![]() ![]() You can put this solution on YOUR website! .\r \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "These methods are Substitution, Elimination, the Determinant method (or Cramer's rule).\r \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " This general criterion has many modifications.\r \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |