document.write( "Question 938455: How would I use the elimination method to for this equation?
\n" ); document.write( "5r+2t=5
\n" ); document.write( "3r-7t=3 \n" ); document.write( "

Algebra.Com's Answer #571727 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "We want to eliminate a letter.\r\n" );
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document.write( "5r+2t = 5\r\n" );
document.write( "3r-7t = 3\r\n" );
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document.write( "Let's choose r to eliminate.\r\n" );
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document.write( "The coefficient of r in the first equation is 5.\r\n" );
document.write( "The coefficient of r in the second equation is 3.\r\n" );
document.write( "The least common multiple of 5 and 3 is 15.  \r\n" );
document.write( "We want the terms in r to be equal in magnitude\r\n" );
document.write( "but opposite in sign.  To do that, we multiply both\r\n" );
document.write( "sides of the first equiation by -3 and both sides\r\n" );
document.write( "of the second equation by 5.  We get\r\n" );
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document.write( "-3(5r+2t) = -3(5)\r\n" );
document.write( " 5(3r-7t) =  5(3)\r\n" );
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document.write( " -15r- 6t = -15\r\n" );
document.write( "  15r-35t =  15\r\n" );
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document.write( "Next we add them vertically, term by term:\r\n" );
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document.write( " -15r- 6t = -15\r\n" );
document.write( "  15r-35t =  15\r\n" );
document.write( "--------------\r\n" );
document.write( "   0r-41t =   0\r\n" );
document.write( "     -41t =   0\r\n" );
document.write( "    \r\n" );
document.write( "Divide both sides by -41\r\n" );
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document.write( "  = \r\n" );
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document.write( "        t = 0\r\n" );
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document.write( "Substitute 0 for t in either one of the \r\n" );
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document.write( "    5r+2t = 5  \r\n" );
document.write( "  5r+2(0) = 5\r\n" );
document.write( "     5r+0 = 5\r\n" );
document.write( "       5r = 5\r\n" );
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document.write( "Divide both sides by 5\r\n" );
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document.write( "     = \r\n" );
document.write( "        \r\n" );
document.write( "        r = 1\r\n" );
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document.write( "Solution (r,t) = (1,0)\r\n" );
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document.write( "Edwin

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