document.write( "Question 145910This question is from textbook Intermediate Algebra
\n" ); document.write( ": Will someone help me to solve the system of equations by using addition (elimination)method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions.\r
\n" ); document.write( "\n" ); document.write( "2x – 7y = 3
\n" ); document.write( "-4x + 14y = -9\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #106480 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Will someone help me to solve the system of equations by using addition (elimination)method. If the answer is a unique solution, present it as an ordered pair: (x, y). If not, specify whether the answer is \"no solution\" or \"infinitely many solutions.
\n" ); document.write( "

\r\n" );
document.write( " 2x –  7y =  3\r\n" );
document.write( "-4x + 14y = -9 \r\n" );
document.write( "\r\n" );
document.write( "To make the y's cancel, multiply the top equation \r\n" );
document.write( "through by 2:  4x - 14y = 6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 4x - 14y =  6\r\n" );
document.write( "-4x + 14y = -9\r\n" );
document.write( "\r\n" );
document.write( "Now add vertically term by term:\r\n" );
document.write( "\r\n" );
document.write( " 4x - 14y =  6\r\n" );
document.write( "-4x + 14y = -9\r\n" );
document.write( "--------------\r\n" );
document.write( "        0 = -3\r\n" );
document.write( "\r\n" );
document.write( "All the variables canceled out and left a FALSE \r\n" );
document.write( "numerical equation.  Therefore there is no solution,\r\n" );
document.write( "and the system is called \"inconsistent\".\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "However if you had had this system of equations instead,\r\n" );
document.write( "where there were a -6 where the -9 is:\r\n" );
document.write( "\r\n" );
document.write( " 2x –  7y =  3\r\n" );
document.write( "-4x + 14y = -6 \r\n" );
document.write( "\r\n" );
document.write( "To make the y's cancel, you would, as above multiply the \r\n" );
document.write( "top equation through by 2:  4x - 14y = 6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " 4x - 14y =  6\r\n" );
document.write( "-4x + 14y = -6\r\n" );
document.write( "\r\n" );
document.write( "Now as above, you would add vertically term by term:\r\n" );
document.write( "\r\n" );
document.write( " 4x - 14y =  6\r\n" );
document.write( "-4x + 14y = -6\r\n" );
document.write( "--------------\r\n" );
document.write( "        0 =  0\r\n" );
document.write( "\r\n" );
document.write( "As above, all the variables canceled out, but this time\r\n" );
document.write( "we are left with a TRUE numerical equation.  Therefore \r\n" );
document.write( "there are infinitely many solutions, and the system\r\n" );
document.write( "is called \"dependent\".\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );