document.write( "Question 262455: I am trying to help my niece with her homework and I need step-by-step instructions on how to use substitution to solve a system of equations.
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Algebra.Com's Answer #193379 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\"system%282x+%2B+3y+=+5%2C%0D%0A4x+-+9y+=+9%29\"
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document.write( "Substitution is the worst way to solve a system which\r\n" );
document.write( "does not have any letters with coefficient of 1 or -1.\r\n" );
document.write( "Such systems are much easier solved by elimination.\r\n" );
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document.write( "However, since you specified to do it by substitution,\r\n" );
document.write( "I will do so, but it will be much more difficult, as\r\n" );
document.write( "it will involve lots of work with fractions. Here goes:\r\n" );
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document.write( "Solve the first equation for x\r\n" );
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document.write( "\"2x%2B3y=5\"\r\n" );
document.write( "\"2x=5-3y\"\r\n" );
document.write( "\"x=%285-3y%29%2F2\"\r\n" );
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document.write( "Substitute \"%285-3y%29%2F2\" for \"x\"\r\n" );
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document.write( "\"4x+-+9y+=+9\"\r\n" );
document.write( "\"4%28%285-3y%29%2F2%29-9y=9\"\r\n" );
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document.write( "Cancel the 2 into the 4 and get a 2 where the 4 is\r\n" );
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document.write( "\"%22%22%5E2\"\"cross%284%29%28%285-3y%29%2Fcross%282%29%29-9y=9\"\r\n" );
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document.write( "\"2%285-3y%29-9y=9\"\r\n" );
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document.write( "Distribute to remove the parentheses:\r\n" );
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document.write( "\"10-6y-9y=9\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"10-15y=9\"\r\n" );
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document.write( "Add -10 to both sides:\r\n" );
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document.write( "\"-15y=-1\"\r\n" );
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document.write( "Divide both sides by \"-15\"\r\n" );
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document.write( "\"%28-15y%29%2F%28-15%29=%28-1%29%2F%28-15%29\"\r\n" );
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document.write( "Cancel the \"-15\"'s, and simplify the right side\r\n" );
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document.write( "\"%28cross%28-15%29y%29%2F%28cross%28-15%29%29=1%2F15\"\r\n" );
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document.write( "\"y=1%2F15\"\r\n" );
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document.write( "Now we substitute \"1%2F15\" for \"y\" into\r\n" );
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document.write( "\"x=%285-3y%29%2F2\"\r\n" );
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document.write( "\"x=%285-3%281%2F15%29%29%2F2\"\r\n" );
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document.write( "Cancel the 3 into the \"15\"\r\n" );
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document.write( "\"x=%285-cross%283%29%281%2Fcross%2815%29%5B5%5D%29%29%2F2\"\r\n" );
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document.write( "\"x=%285-1%2F5%29%2F2\"\r\n" );
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document.write( "Simplify the compound fraction by multiplying\r\n" );
document.write( "the numerator and denominator by the LCD of 5\r\n" );
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document.write( "\"x=%285%2A%285-1%2F5%29%29%2F%285%2A2%29\"\r\n" );
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document.write( "Distribute the 5 into the parentheses, and write 10 for the\r\n" );
document.write( "denominator \"5%2A2\":\r\n" );
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document.write( "\"x=%285%2A5-5%2A%281%2F5%29%29%2F10\"\r\n" );
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document.write( "Write 25 for 5*5 and cancel the 5's in the second\r\n" );
document.write( "term on top:\r\n" );
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document.write( "\"x=%2825-cross%285%29%2A%281%2Fcross%285%29%29%29%2F10\"\r\n" );
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document.write( "\"x=%2825-1%29%2F10\"\r\n" );
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document.write( "\"x=24%2F10\"\r\n" );
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document.write( "We reduce the fraction:\r\n" );
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document.write( "\"x=12%2F5\"\r\n" );
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document.write( "So the solution is \"x=12%2F5\", \"y=1%2F15\"\r\n" );
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document.write( "But that is by far the hardest way to solve a \r\n" );
document.write( "system of equations which has none of the terms\r\n" );
document.write( "x, -x, y, or -y.  The easist way would be the\r\n" );
document.write( "elimination method.  \r\n" );
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document.write( "Edwin
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