document.write( "Question 934976: Solve using Cramer’s rule 3x-y+2z=13, 2x+y-z=3, x+3y-5z=-8 \n" ); document.write( "
Algebra.Com's Answer #568021 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "3x-y+2z=13 \r\n" );
document.write( "2x+y-z=3 \r\n" );
document.write( "x+3y-5z=-8\r\n" );
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document.write( "Below is one solved exactly like yours. Use it as a model to solve \r\n" );
document.write( "yours.\r\n" );
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document.write( "Whenever one of your equations has x with coefficient 1 or -1,\r\n" );
document.write( "it makes it easier to write that equation first. Since your \r\n" );
document.write( "3rd equation has x with an understood coefficient of 1, it will \r\n" );
document.write( "be easier if you write it first, like this, swapping the 1st and \r\n" );
document.write( "3rd equations so that it is at the top.\r\n" );
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document.write( "x+3y-5z=-8\r\n" );
document.write( "2x+y-z=3\r\n" );
document.write( "3x-y+2z=13\r\n" );
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document.write( "BTW, yours has solution (x,y,z) = (3,-2,1)\r\n" );
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document.write( "Here's one just like yours. Just use your numbers instead:\r\n" );
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document.write( "x+y+z=6\r\n" );
document.write( "2x-y+z=3\r\n" );
document.write( "x+2y-3z=-4\r\n" );
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document.write( "To solve using Cramer's rule\r\n" );
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document.write( "Write in all the 1 and -1 coefficients:\r\n" );
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document.write( "There are 4 columns,\r\n" );
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document.write( "1. The column of x-coefficients \r\n" );
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document.write( "2. The column of y-coefficients \r\n" );
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document.write( "3. The column of z-coefficients  \r\n" );
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document.write( "4. The column of constants:     \r\n" );
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document.write( "There are four determinants:\r\n" );
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document.write( "1. The determinant  consists of just the three columns\r\n" );
document.write( "of x, y, and z coefficients. in that order, but does not\r\n" );
document.write( "contain the column of constants.\r\n" );
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document.write( "It has value .  I'm assuming you know how to find the\r\n" );
document.write( "value of a 3x3 determinant, for that's a subject all by itself.\r\n" );
document.write( "If you don't know how, post again asking how. \r\n" );
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document.write( "2. The determinant  is like the determinant \r\n" );
document.write( "except that the column of x-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of x-coefficients.\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "3. The determinant  is like the determinant \r\n" );
document.write( "except that the column of y-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of y-coefficients.\r\n" );
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document.write( ".\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "4. The determinant  is like the determinant \r\n" );
document.write( "except that the column of z-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of z-coefficients.\r\n" );
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document.write( ".\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "Now the formulas for x, y and z are\r\n" );
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document.write( "[To read about the 18th century Swiss mathematician Gabriel Cramer \r\n" );
document.write( "who invented Cramer's rule, go here: \r\n" );
document.write( "http://en.wikipedia.org/wiki/Gabriel_Cramer\r\n" );
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document.write( "Edwin
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