document.write( "Question 169709This question is from textbook elementary and Intermediate algebra concepts and application
\n" ); document.write( ": Explain how to apply elimination in solving a system of equations.
\n" ); document.write( "a. Explain how to apply substitution in solving a system of equations.
\n" ); document.write( "b. Demonstrate each technique in solving the system
\n" ); document.write( "3x + 9y = 12
\n" ); document.write( "5x - 4y = 3
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Algebra.Com's Answer #125245 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Explain how to apply elimination in solving a system of equations.
\n" ); document.write( "a. Explain how to apply substitution in solving a system of equations.
\n" ); document.write( "b. Demonstrate each technique in solving the system\r
\n" ); document.write( "\n" ); document.write( "\"system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29\"\r
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document.write( "By elimination:\r\n" );
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document.write( "First eliminate \"x\" and find \"y\".\r\n" );
document.write( "Multiply the first equation through by \"-5\" \r\n" );
document.write( "and the second equation through by \"3\":\r\n" );
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document.write( "\"system%28-15x+-45y+=+-60%2C15x+-+12y+=+9%29\"\r\n" );
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document.write( "Now add vertically term by term:\r\n" );
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document.write( "\"-57y=-51\"\r\n" );
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document.write( "Divide both sides by \"-57\"\r\n" );
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document.write( "\"y=%28-51%29%2F%28-57%29\"\r\n" );
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document.write( "\"y=17%2F19\"\r\n" );
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document.write( "----\r\n" );
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document.write( "\"system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29\"\r\n" );
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document.write( "Next eliminate \"y\" and find \"x\".\r\n" );
document.write( "Multiply the first equation through by \r\n" );
document.write( "\"4\" and the second equation through \r\n" );
document.write( "by \"9\":\r\n" );
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document.write( "\"system%2812x+%2B36y+=+48%2C45x+-+36y+=+27%29\"\r\n" );
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document.write( "Now add vertically term by term:\r\n" );
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document.write( "\"57x=75\"\r\n" );
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document.write( "Divide both sides by \"57\"\r\n" );
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document.write( "\"x=75%2F57\"\r\n" );
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document.write( "\"x=25%2F19\"\r\n" );
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document.write( "Solution:   \r\n" );
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document.write( "-------------------\r\n" );
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document.write( "Now do the same problem from scratch using\r\n" );
document.write( "substitution:\r\n" );
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document.write( "\"system%283x+%2B+9y+=+12%2C5x+-+4y+=+3%29\"\r\n" );
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document.write( "Solve the first equation for \"x\":\r\n" );
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document.write( "\"3x+%2B+9y+=+12\"\r\n" );
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document.write( "Add \"-9x\" to both sides:\r\n" );
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document.write( "\"3x=12-9y\"\r\n" );
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document.write( "Divide through every term by 3:\r\n" );
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document.write( "\"%283x%29%2F3=12%2F3-%289y%29%2F3\"\r\n" );
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document.write( "Simplify:\r\n" );
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document.write( "\"x=4-3y\"\r\n" );
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document.write( "Substitute \"%284-3y%29\" for \"x\"\r\n" );
document.write( "in the second equation:\r\n" );
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document.write( "\"5x+-+4y+=+3%29\"\r\n" );
document.write( "\"5%284-3y%29+-+4y+=+3%29\"\r\n" );
document.write( "Distribute:\r\n" );
document.write( "\"20-15y-4y=3\"\r\n" );
document.write( "\"20-19y=3\"\r\n" );
document.write( "Add \"-20\" to both sides:\r\n" );
document.write( "\"-19y=3-20\"\r\n" );
document.write( "\"-19y=-17\"\r\n" );
document.write( "Divide both sides by \"-19\"\r\n" );
document.write( "\"%28-19y%29%2F%28-19%29=%28-17%29%2F%28-19%29\"\r\n" );
document.write( "\"y=17%2F19\"\r\n" );
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document.write( "Now substitute \"%2817%2F19%29\" for \"y\"\r\n" );
document.write( "in\r\n" );
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document.write( "\"x=4-3y\"\r\n" );
document.write( "\"x=4-3%2817%2F19%29\"\r\n" );
document.write( "Write the \"4\" as \"4%2F1\" and \r\n" );
document.write( "write the \"3\" as \"3%2F1\"\r\n" );
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document.write( "\"x=4%2F1-%283%2F1%29%2817%2F19%29\"\r\n" );
document.write( "\"x=4%2F1-51%2F19\"\r\n" );
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document.write( "The LCD is \"19\"\r\n" );
document.write( "Multiply the \"4%2F1\" by \"19%2F19\"\r\n" );
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document.write( "\"x=%284%2F1%29%2819%2F19%29-51%2F19\"\r\n" );
document.write( "\"x=76%2F19-51%2F19\"\r\n" );
document.write( "\"x=25%2F19\"\r\n" );
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document.write( "Solution:  \r\n" );
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document.write( "Edwin
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