\r\n" );
document.write( "I'll do it both ways:\r\n" );
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document.write( "By Cramer's rule:\r\n" );
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document.write( "
\r\n" );
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document.write( " 1x + 5y = 7\r\n" );
document.write( "-2x - 7y = -5\r\n" );
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document.write( "Form the determinant D which is the\r\n" );
document.write( "coefficients as they appear left of\r\n" );
document.write( "the equal sign when in general form:\r\n" );
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document.write( "
\r\n" );
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document.write( "The \"column of constants\" is 
, consisting of the numbers\r\n" );
document.write( "right of the equal signs is not used in the determinant D \r\n" );
document.write( "but is used in the other two determinants.\r\n" );
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document.write( "Dx is formed by replacing the FIRST column of D (the \r\n" );
document.write( "coefficients of x, the FIRST variable) by the column of constants:\r\n" );
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document.write( "
\r\n" );
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document.write( "Dy is formed by replacing the SECOND column of D (the \r\n" );
document.write( "coefficients of y, the SECOND variable) by the column of constants:\r\n" );
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document.write( "
\r\n" );
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document.write( "Then:\r\n" );
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\r\n" );
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document.write( "
\r\n" );
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document.write( "So we see that x = -8 and y = 3\r\n" );
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document.write( "The solution is (x,y) = (-8,3)\r\n" );
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document.write( "By matrix inversion:\r\n" );
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document.write( " 1x + 5y = 7\r\n" );
document.write( "-2x - 7y = -5\r\n" );
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document.write( "Form the matrix equation:\r\n" );
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document.write( "
\r\n" );
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document.write( "Now we find the inverse of the coefficient matrix 
\r\n" );
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document.write( "To find the inverse of a 2x2 matrix: \r\n" );
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document.write( "1. find the determinant of the matrix:\r\n" );
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=\r\n" );
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document.write( "[Note that this is exactly the same as the determinant D in Cramer's rule\r\n" );
document.write( "above.]\r\n" );
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document.write( "2. Swap the upper left and lower right elements:\r\n" );
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\r\n" );
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document.write( "3. Change the signs of the upper right and lower left elements:\r\n" );
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\r\n" );
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document.write( "4. Divide every term by the value of the determinant in step 1, which is 3.\r\n" );
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\r\n" );
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document.write( "Now go back to the matrix equation\r\n" );
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document.write( " \r\n" );
document.write( "Multiply the inverse matrix on the left of the\r\n" );
document.write( "left side and also on the left of the right side;\r\n" );
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document.write( "
\r\n" );
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document.write( "I assume you know how to multiply matrices. If you\r\n" );
document.write( "don't, post again asking how to. Multiply the first\r\n" );
document.write( "two matrices on the left, and multiply the matrices on\r\n" );
document.write( "the right:\r\n" );
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document.write( " 
\r\n" );
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document.write( "We have the identity matrix on the left to multiply by\r\n" );
document.write( "the matrix 
which just gives:\r\n" );
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document.write( " 
\r\n" );
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document.write( "So we see that x = -8 and y = 3.\r\n" );
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document.write( "The solution is (x,y) = (-8,3)\r\n" );
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document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
