document.write( "Question 215479: Solve by using the elimination method\r
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\n" ); document.write( "\n" ); document.write( "0.3x-0.2y=4
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Algebra.Com's Answer #162828 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
$\"system%280.3x-0.2y=4%2C+0.5x%2B0.3y=71%2F23%29\"$
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document.write( "You must clear the first of decimals, and\r\n" );
document.write( "you must clear the second equation of both\r\n" );
document.write( "decimals and fractions.\r\n" );
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document.write( "To clear the first equation of decimals we\r\n" );
document.write( "multiply each term through by 10, and get\r\n" );
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document.write( "We clear the second equation first of fractions\r\n" );
document.write( "by multiplying each term by 23:\r\n" );
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document.write( "To clear this equation of decimals we\r\n" );
document.write( "multiply each term through by 10, and get\r\n" );
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document.write( "So the system is now:\r\n" );
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document.write( "We find the least common multiple of the\r\n" );
document.write( "absolute value of the coefficients of x.\r\n" );
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document.write( "The least common multiple of 3 and 115 is\r\n" );
document.write( "their product 345.\r\n" );
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document.write( "We divide 3 into 345 and get 115, so we\r\n" );
document.write( "multiply the first equation by 115:\r\n" );
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document.write( "Now we divide 115 into 345 and get 3, so we\r\n" );
document.write( "multiply the second equation by -3.  We\r\n" );
document.write( "choose to multiply by a negative number so\r\n" );
document.write( "they will cancel as you will see\r\n" );
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document.write( "Now we have this system:\r\n" );
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document.write( "We can add the two equations vertically, term\r\n" );
document.write( "by term, and the  in the first equation\r\n" );
document.write( "cancels with the  term in the second.\r\n" );
document.write( "Upon adding corresponding terms:\r\n" );
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document.write( "or just\r\n" );
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document.write( "So we divide both sides by \r\n" );
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document.write( "That fraction reduces by dividing top and\r\n" );
document.write( "bottom by 19:\r\n" );
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document.write( "Now we must find x.  In many equations we\r\n" );
document.write( "would subsatitute the value of x into\r\n" );
document.write( "one of the equations.  However since the\r\n" );
document.write( "value for y is such an ugly fraction, we\r\n" );
document.write( "start back with this system:\r\n" );
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document.write( "This time we find the least common multiple of the\r\n" );
document.write( "absolute value of the coefficients of y.\r\n" );
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document.write( "The least common multiple of 2 and 69 is\r\n" );
document.write( "their product 138.\r\n" );
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document.write( "We divide 2 into 138 and get 69, so we\r\n" );
document.write( "multiply the first equation by 69:\r\n" );
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document.write( "Now we divide 69 into 138 and get 2, so we\r\n" );
document.write( "multiply the second equation by 2.  We don't\r\n" );
document.write( "need to multiply by a negative number this time\r\n" );
document.write( "because the y terms are already opposit5 in\r\n" );
document.write( "sing and so they will cancel.\r\n" );
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document.write( "Now we have this system:\r\n" );
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document.write( "We can add the two equations vertically, term\r\n" );
document.write( "by term, and the  in the first equation\r\n" );
document.write( "cancels with the  term in the second.\r\n" );
document.write( "Upon adding corresponding terms:\r\n" );
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document.write( "\r\n" );
document.write( "or just\r\n" );
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document.write( "So we divide both sides by \r\n" );
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document.write( "That fraction reduces by dividing top and\r\n" );
document.write( "bottom by 19\r\n" );
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document.write( "So the solution is\r\n" );
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document.write( "Edwin
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