document.write( "Question 865898: Find z by the use of determinant : 3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0 \n" ); document.write( "
Algebra.Com's Answer #521993 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "3x-4y+2z+8=0, x+5y-3z+2=0, 5x+3y-z+6=0\r\n" );
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document.write( "Get the constants on the right:\r\n" );
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document.write( "3x-4y+2z=-8, x+5y-3z=-2, 5x+3y-z=-6\r\n" );
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document.write( "I'll color the constants red:\r\n" );
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document.write( "\"system%283x-4y%2B2z=red%28-8%29%2Cx%2B5y-3z=red%28-2%29%2C5x%2B3y-z=red%28-6%29%29\"\r\n" );
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document.write( "\"D=abs%28matrix%283%2C3%2C%0D%0A3%2C-4%2C+2%2C%0D%0A1%2C+5%2C+-3%2C%0D%0A5%2C+3%2C+-1%29%29\" \r\n" );
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document.write( "x is the FIRST unknown and so \"D%5Bx%5D\" is just like \"D\"\r\n" );
document.write( "except that the FIRST column is replaced by the three red numbers: \r\n" );
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document.write( "y is the SECOND unknown and so \"D%5By%5D\" is just like \"D\"\r\n" );
document.write( "except that the SECOND column is replaced by the three red numbers: \r\n" );
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document.write( "z is the THIRD unknown and so \"D%5Bz%5D\" is just like \"D\"\r\n" );
document.write( "except that the THIRD column is replaced by the three red numbers,\r\n" );
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document.write( "Do you know how to evaluate a 3x3 determinant?\r\n" );
document.write( "If not, post again asking how to.  I will assume\r\n" );
document.write( "you already know how.\r\n" );
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document.write( "\"D=24\"\r\n" );
document.write( "\"D%5Bx%5D=-48\"\r\n" );
document.write( "\"D%5By%5D=72\"\r\n" );
document.write( "\"D%5Bz%5D=120\"\r\n" );
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document.write( "Then the solutions are:\r\n" );
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document.write( "\"x=D%5Bx%5D%2FD=%28-48%29%2F24+=+-2\"\r\n" );
document.write( "\"y=D%5By%5D%2FD=%2872%29%2F24+=+3\"\r\n" );
document.write( "\"z=D%5Bz%5D%2FD=%28120%29%2F24+=+5\"\r\n" );
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document.write( "Edwin
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