document.write( "Question 1177923: Solve the linear systems using any method of your choice.
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document.write( "2x-y=1
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document.write( "4x-2y=2 \n" );
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Algebra.Com's Answer #807073 by ikleyn(52775)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "Consider the extended matrix. \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "It is easy to see that its rows are proportional.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "It means that one equation is equivalent to the other equation,\r\n" ); document.write( "\r\n" ); document.write( "so FACTUALLY you have only one equation in two unknowns.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Such system has INFINITELY MANY solutions.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "Take x as a FREE variable and express y = 2x-1 from the first equation.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "You may give any value to x and calculate the respective value of y: each such a pair (x,y) will be a solution.\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( "Solved and explained.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "-------------\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "See the lesson\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.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |