document.write( "Question 528396: linear algebra elimination method
\n" ); document.write( "13) 2/3x+2/5y=4/5
\n" ); document.write( " 1/2x+2/3y=-1/2\r
\n" ); document.write( "\n" ); document.write( "12)9/14x+y=19/7
\n" ); document.write( " -20x+21y=144\r
\n" ); document.write( "\n" ); document.write( "11)x+5/3y=7/3
\n" ); document.write( " 2/5x-y=3/5\r
\n" ); document.write( "\n" ); document.write( "10)x+9/4y=7/4
\n" ); document.write( " 5/9x-y=2/9\r
\n" ); document.write( "\n" ); document.write( "8)18x-3y=-3
\n" ); document.write( " 6x+7y=39\r
\n" ); document.write( "\n" ); document.write( "6)15x+14y=2
\n" ); document.write( " 12x-6y=-7 \n" ); document.write( "

Algebra.Com's Answer #349274 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "I'll just do this one: \r\n" );
document.write( "\r\n" );
document.write( " x + y = \r\n" );
document.write( " -20x + 21y = 144\r\n" );
document.write( "\r\n" );
document.write( "To clear the first one of fractions multiply \r\n" );
document.write( "every term by the LCD of 14:\r\n" );
document.write( "\r\n" );
document.write( "14·x + 14·y = 14·\r\n" );
document.write( "  \r\n" );
document.write( "9x + 14y = 38\r\n" );
document.write( "\r\n" );
document.write( "Now we have the system:\r\n" );
document.write( "\r\n" );
document.write( "  9x + 14y =  38\r\n" );
document.write( "-20x + 21y = 144\r\n" );
document.write( "\r\n" );
document.write( "The idea is to eliminate a variable:\r\n" );
document.write( "The coefficients of y are 14 and 21\r\n" );
document.write( "The least common multiple of 14 and 21\r\n" );
document.write( "is 42.  To make the coefficients of\r\n" );
document.write( "y equal in absolute value yet opposite\r\n" );
document.write( "in sign we multiply the first equation\r\n" );
document.write( "through by -3 and the second equation\r\n" );
document.write( "through by 2.  That will make the\r\n" );
document.write( "coefficients -42 and +42:\r\n" );
document.write( "\r\n" );
document.write( "-3[  9x + 14y] = -3[38]\r\n" );
document.write( " 2[-20x + 21y] =  2[144]\r\n" );
document.write( "\r\n" );
document.write( "   -27x - 42y = -114\r\n" );
document.write( "   -40x + 42y =  288\r\n" );
document.write( "\r\n" );
document.write( "Now we add those term by term:\r\n" );
document.write( "\r\n" );
document.write( "   -27x - 42y = -114\r\n" );
document.write( "   -40x + 42y =  288\r\n" );
document.write( "  -------------------\r\n" );
document.write( "   -67x       =  174\r\n" );
document.write( "      x       =  \r\n" );
document.write( "\r\n" );
document.write( "Since that is too complicated a fraction to\r\n" );
document.write( "substitute, we will start over and eliminate x:\r\n" );
document.write( "\r\n" );
document.write( "---------------------------\r\n" );
document.write( "       \r\n" );
document.write( "  9x + 14y =  38\r\n" );
document.write( "-20x + 21y = 144\r\n" );
document.write( "\r\n" );
document.write( "Next we eliminate the other variable x:\r\n" );
document.write( "The coefficients of x are 9 and -20\r\n" );
document.write( "The least common multiple of 9 and 20\r\n" );
document.write( "is 180.  To make the coefficients of\r\n" );
document.write( "x equal in absolute value yet opposite\r\n" );
document.write( "in sign we multiply the first equation\r\n" );
document.write( "through by 20 and the second equation\r\n" );
document.write( "through by 9.  That will make the\r\n" );
document.write( "coefficients +180 and -180:\r\n" );
document.write( "\r\n" );
document.write( "20[  9x + 14y] = 20[38]\r\n" );
document.write( " 9[-20x + 21y] =  9[144]\r\n" );
document.write( "\r\n" );
document.write( "   180x + 280y =  760\r\n" );
document.write( "  -180x + 189y = 1296\r\n" );
document.write( "\r\n" );
document.write( "Now we add those term by term:\r\n" );
document.write( "\r\n" );
document.write( "   180x + 280y =  760\r\n" );
document.write( "  -180x + 189y = 1296\r\n" );
document.write( "  -------------------\r\n" );
document.write( "          469y = 2056\r\n" );
document.write( "             y = \r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
document.write( "\r\n" );
document.write( "So the solution is \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );