document.write( "Question 811434: Use addition to solve. \r
\n" ); document.write( "\n" ); document.write( "2x + 3y = -5
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\n" ); document.write( "\n" ); document.write( "I know the answer is (7,0), but how to do I come to that answer? \n" ); document.write( "
Algebra.Com's Answer #488738 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2x + 3y = -5\r\n" );
document.write( "3x - 2y = 12\r\n" );
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document.write( "The answer is not (7,0).  You must have looked at the\r\n" );
document.write( "answer to the wrong problem.\r\n" );
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document.write( "We look at the two coefficients of y.  They are +3 in the first\r\n" );
document.write( "equation and -2 in the second. The least common multiple of |+3|\r\n" );
document.write( "and |-2| is 6.  \r\n" );
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document.write( "So if we multiply both sides of the first equation by 2 and \r\n" );
document.write( "both sides of the second equation by 3, we get\r\n" );
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document.write( " 4x + 6y = -10\r\n" );
document.write( " 9x - 6y =  36\r\n" );
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document.write( "Now when we add equals to equals, the +6y in the first will cancel\r\n" );
document.write( "with the -6y in the second:\r\n" );
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document.write( " 4x + 6y = -10\r\n" );
document.write( " 9x - 6y =  36 \r\n" );
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document.write( "13x      =  26\r\n" );
document.write( "  x      =  2\r\n" );
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document.write( "Then we substitute that in either or the original equations:\r\n" );
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document.write( "  2x + 3y = -5\r\n" );
document.write( "2(2) + 3y = -5\r\n" );
document.write( "   4 + 3y = -5\r\n" );
document.write( "       3y = -9\r\n" );
document.write( "        y = -3\r\n" );
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document.write( "So the answer is (2,-3).\r\n" );
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document.write( "Checking the first equation:\r\n" );
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document.write( "     2x + 3y = -5\r\n" );
document.write( "2(2) + 3(-3) = -5\r\n" );
document.write( "       4 - 9 = -5 \r\n" );
document.write( "          -5 = -5\r\n" );
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document.write( "Checking the second equation:\r\n" );
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document.write( "     3x - 2y = 12\r\n" );
document.write( "3(2) - 2(-3) = 12\r\n" );
document.write( "       6 + 6 = 12\r\n" );
document.write( "          12 = 12\r\n" );
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document.write( "So the answer is (2,-3), not (7,0).\r\n" );
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document.write( "Edwin
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