document.write( "Question 122173This question is from textbook
\n" ); document.write( ": Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B)\r
\n" ); document.write( "\n" ); document.write( "x+8y=-29
\n" ); document.write( "6x+2y=10 \n" ); document.write( "
Algebra.Com's Answer #89699 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Solve the following system of equations by using the inverse of the coefficient matrix A. (AX=B) \r
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document.write( "  x + 4y = 22\r\n" );
document.write( "-6x + 5y = 13\r\n" );
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document.write( "Form the matrix equation:\r\n" );
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\n" ); document.write( "Now we must find the inverse of the coefficient matrix \"%28matrix%282%2C2%2C1%2C4%2C-6%2C5%29%29\"\r
\n" ); document.write( "\n" ); document.write( "To find the inverse of a 2x2 matrix: \r
\n" ); document.write( "\n" ); document.write( "1. find the determinant of the matrix:
\n" ); document.write( "\"abs%28matrix%282%2C2%2C1%2C4%2C-6%2C5%29%29%29=%281%29%285%29-%284%29%28-6%29\"=\"5%2B24=29\"
\n" ); document.write( "2. Swap the upper left and lower right elements
\n" ); document.write( "\"%28matrix%282%2C2%2C5%2C4%2C-6%2C1%29%29\"
\n" ); document.write( "3. Change the signs of the upper right and lower left elements
\n" ); document.write( "\"%28matrix%282%2C2%2C5%2C-4%2C6%2C1%29%29\"
\n" ); document.write( "4. Divide every term by the value of the determinant, which is 29.
\n" ); document.write( "\"%28matrix%282%2C2%2C5%2F29%2C-4%2F29%2C6%2F29%2C1%2F29%29%29\"
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document.write( "Now go back to the matrix equation\r\n" );
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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( "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( "We have the identity matrix on the left to multiply by\r\n" );
document.write( "the matrix \"%28matrix%282%2C1%2Cx%2Cy%29%29\" which just gives:\r\n" );
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document.write( "                \"%28matrix%282%2C1%2Cx%2Cy%29%29=%28matrix%282%2C1%2C2%2C5%29%29\"\r\n" );
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document.write( "So we see that x = 2 and y = 5.\r\n" );
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document.write( "Edwin
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