document.write( "Question 858091: x+y-2z=3
\n" ); document.write( "3x-y+z=5
\n" ); document.write( "3x+3y-6z=9\r
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Algebra.Com's Answer #517097 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi, there--\r\n" );
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document.write( "Your Problem:\r\n" );
document.write( "Solve the following system of linear equations using Cramer's Rule.\r\n" );
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document.write( "Solution:\r\n" );
document.write( "Cramer's Rule is a solution method that uses matrices and their determinants.\r\n" );
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document.write( "Step 1: Write the coefficient matrix and the answer column for your system.\r\n" );
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document.write( "Step 2: Now we find find the determinants of four matrices, , , , and .\r\n" );
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document.write( "Matrix D is the coefficient matrix.\r\n" );
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document.write( "The determinant, |D| = 48\r\n" );
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document.write( "Matrix Dx is the coefficient matrix with column one replaced with the answer column.\r\n" );
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document.write( "The determinant, |Dx| = 96\r\n" );
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document.write( "Matrix Dy is the coefficient matrix with column two replaced with the answer column.\r\n" );
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document.write( "The determinant, |Dy| = 48\r\n" );
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document.write( "Matrix Dz is the coefficient matrix with column three replaced with the answer column.\r\n" );
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document.write( "The determinant, |Dz| = 0\r\n" );
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document.write( "Step 3. Now that we have these values, we can find x, y, and z.\r\n" );
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document.write( "x = Dx / D = 96/48 = 2\r\n" );
document.write( "y = Dy / D = 48/48 = 1\r\n" );
document.write( "z = Dz / D = 0/48 = 0\r\n" );
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document.write( "Check your answer by substituting 2 for x, 1 for y, and 0 for z in the original equations. \r\n" );
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document.write( "2x + y - z = 3\r\n" );
document.write( "(2) + (1) - 2(0) = 3\r\n" );
document.write( "2 + 1 = 3\r\n" );
document.write( "3 = 3\r\n" );
document.write( "Check!\r\n" );
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document.write( "3x - y + z = 5\r\n" );
document.write( "3(2) - (1) + (0) = 5\r\n" );
document.write( "6 - 1 = 5\r\n" );
document.write( "5 = 5\r\n" );
document.write( "Check!\r\n" );
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document.write( "3x + 3y - 6z = 9\r\n" );
document.write( "3(2) + 3(1) - 6(0) = 9\r\n" );
document.write( "6 + 3 = 9\r\n" );
document.write( "9 = 9\r\n" );
document.write( "Check!\r\n" );
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document.write( "Hope this helps. If you have questions about how to find the determinant of a matrix, here is a nice explanation at PurpleMath:\r\n" );
document.write( "http://www.purplemath.com/modules/determs2.htm\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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