document.write( "Question 94795: x+y=11 Use Cramer's rule to solve the x-y=5 following system of equations. If D=0, use another method to solve the system. \n" ); document.write( "
Algebra.Com's Answer #69005 by Edwin McCravy(20060)\"\" \"About 
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\n" ); document.write( "x+y=11 Use Cramer's rule to solve the x-y=5 following system of equations. If D=0, use another method to solve the system.
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document.write( "To solve the system of equations by Cramer's rule:\r\n" );
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document.write( "\"Ax%2BBy=C\"\r\n" );
document.write( "\"Px%2BQy=R\"\r\n" );
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document.write( "D is the matrix of coefficients as they appear\r\n" );
document.write( "on the left of the equal sign:\r\n" );
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document.write( "D = \"%28matrix%282%2C2%2CA%2CB%2CP%2CQ%29%29\" = \"AQ-BP\"\r\n" );
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document.write( "Dx is the matrix which is like D except that,\r\n" );
document.write( "   since x is the FIRST unknown letter, it has\r\n" );
document.write( "   its FIRST column \"matrix%282%2C1%2CA%2CP%29\" replaced \r\n" );
document.write( "   by the column of numbers on the right side of\r\n" );
document.write( "   the equal signs in the original system, \"matrix%282%2C1%2CC%2CR%29\".\r\n" );
document.write( "   So\r\n" );
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document.write( "Dx = \"%28matrix%282%2C2%2CC%2CB%2CR%2CQ%29%29\" = \"CQ-BR\"\r\n" );
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document.write( "Dy is the matrix which is like D except that,\r\n" );
document.write( "   since y is the SECOND unknown letter, it has\r\n" );
document.write( "   its SECOND column \"matrix%282%2C1%2CB%2CQ%29\" replaced \r\n" );
document.write( "   by the column of numbers on the right side of\r\n" );
document.write( "   the equal signs in the original system, \"matrix%282%2C1%2CC%2CR%29\".\r\n" );
document.write( "   So\r\n" );
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document.write( "Dy = \"%28matrix%282%2C2%2CA%2CC%2CP%2CR%29%29\" = \"AR-CP\"\r\n" );
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document.write( "Then x = \"Dx%2FD\" and y = \"Dy%2FD\"\r\n" );
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document.write( " So for your system:\r\n" );
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document.write( "x + y = 11 \r\n" );
document.write( "x - y =  5\r\n" );
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document.write( "Write that as \r\n" );
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document.write( "\"1x%2B1y=11\"\r\n" );
document.write( "\"1x-1y=5\"\r\n" );
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document.write( "D is the matrix of coefficients as they appear\r\n" );
document.write( "on the left of the equal sign:\r\n" );
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document.write( "D = \"%28matrix%282%2C2%2C1%2C1%2C1%2C-1%29%29\" = \"%281%29%28-1%29-%281%29%281%29\" = \"-1-1\" = \"-2\"\r\n" );
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document.write( "==================================================\r\n" );
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document.write( "Dx is the matrix which is like D except that,\r\n" );
document.write( "   since x is the FIRST unknown letter, it has\r\n" );
document.write( "   its FIRST column \"matrix%282%2C1%2C1%2C1%29\" replaced \r\n" );
document.write( "   by the column of numbers on the right side of\r\n" );
document.write( "   the equal signs in the original system, \"matrix%282%2C1%2C11%2C5%29\".\r\n" );
document.write( "   So\r\n" );
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document.write( "Dx = \"%28matrix%282%2C2%2C11%2C1%2C5%2C-1%29%29\" = \"%2811%29%28-1%29-%281%29%285%29\" = \"-11-5\" = \"-16\"\r\n" );
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document.write( "==================================================\r\n" );
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document.write( "Dy is the matrix which is like D except that,\r\n" );
document.write( "   since y is the SECOND unknown letter, it has\r\n" );
document.write( "   its SECOND column \"matrix%282%2C1%2C1%2C-1%29\" replaced \r\n" );
document.write( "   by the column of numbers on the right side of\r\n" );
document.write( "   the equal signs in the original system, \"matrix%282%2C1%2C11%2C5%29\".\r\n" );
document.write( "   So\r\n" );
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document.write( "Dy = \"%28matrix%282%2C2%2C1%2C11%2C1%2C5%29%29\" = \"%281%29%285%29-%2811%29%281%29\" = \"5-11\" = \"-6\"\r\n" );
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document.write( "Then x = \"Dx%2FD\" = \"%28-16%29%2F%28-2%29\" = \"8\" and y = \"Dy%2FD\" = \"%28-6%29%2F%28-2%29\" = \"3\".   \r\n" );
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document.write( "Edwin
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