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document.write( "Hi, there--\r\n" );
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document.write( "Problem:\r\n" );
document.write( "Use Cramer's Rule to solve this system of linear equations: \r\n" );
document.write( "x + 2y = -7\r\n" );
document.write( "2x = 4 + 5y\r\n" );
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document.write( "A Solution:\r\n" );
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document.write( "Cramer's Rule uses the determinant of the coefficient matrix related to this system of \r\n" );
document.write( "equations to find the solution.\r\n" );
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document.write( "First, set up the 2 x 2 coefficient matrix. Write both equations in Ax + By = C form.\r\n" );
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document.write( "x + 2y = -7\r\n" );
document.write( "2x -5y = 4\r\n" );
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document.write( "Now set up the 2 x 2 matrix using the coefficients of the x and y terms.\r\n" );
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document.write( "To find the determinant D, we use the formula,\r\n" );
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document.write( "For your system we have\r\n" );
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document.write( "Now we find two more determinants, 
and 
.\r\n" );
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document.write( "For , we substitute the values on the right side of our equations for the left column of the coefficient matrix.\r\n" );
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\r\n" );
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document.write( "For , we substitute the values on the right side of our equations for the right column of the coefficient matrix.\r\n" );
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\r\n" );
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document.write( "Cramer's Rule states that for the solution to our system of equations (x,y)\r\n" );
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document.write( "and\r\n" );
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document.write( "So, the ordered pair (-3,-2) is the solution to your system of equations.\r\n" );
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document.write( "Let's check this point in our original equations to be sure.\r\n" );
document.write( "x + 2y = -7\r\n" );
document.write( "(-3) + 2(-2) = -7\r\n" );
document.write( "-3 - 4 = -7\r\n" );
document.write( "-7 = -7 \r\n" );
document.write( "CHECK!\r\n" );
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document.write( "2x = 4 + 5y\r\n" );
document.write( "2(-3) = 4 + 5(-2)\r\n" );
document.write( "-6 = 4 - 10\r\n" );
document.write( "-6 = -6 CHECK!\r\n" );
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document.write( "That's it. I hope this helps,\r\n" );
document.write( "Mrs. Figgy\r\n" );
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