document.write( "Question 118383: Find the value of z in the system equations
\n" ); document.write( "2x + 3y - 5z = 3
\n" ); document.write( "x - 2y + z = 0
\n" ); document.write( "3x + y + 3z = 7
\n" ); document.write( "using Cramer's rule. answers(0,4/7,1,10/7)\r
\n" ); document.write( "\n" ); document.write( "Find the value of x in the system of equations
\n" ); document.write( "2x + y - 4 = 0
\n" ); document.write( "13x + (5/2)y - 10 = 0
\n" ); document.write( "using Cramer's rule. (-2,-1,0,1)\r
\n" ); document.write( "\n" ); document.write( "Find the value of y in the system equations
\n" ); document.write( "5x - 3y = 18
\n" ); document.write( "2x + 4y = 2
\n" ); document.write( "using Cramer's rule. (-2,-1,0,1)\r
\n" ); document.write( "\n" ); document.write( "Find the value of y in the system of equations
\n" ); document.write( "2x + 3y - 5z = 3
\n" ); document.write( "x - 2y + z = 0
\n" ); document.write( "3x + y + 3z = 7
\n" ); document.write( "using Cramer's rule
\n" ); document.write( "(0,4/7,1,10/7)\r
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Algebra.Com's Answer #86506 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Find the value of z in the system equations\r\n" );
document.write( "2x + 3y - 5z = 3\r\n" );
document.write( "x - 2y + z = 0\r\n" );
document.write( "3x + y + 3z = 7\r\n" );
document.write( "using Cramer's rule. answers(0,4/7,1,10/7)\r\n" );
document.write( "\r\n" );
document.write( "Write the single letters x, y, and z as\r\n" );
document.write( "1x, 1y, and 1z, so that like terms in the\r\n" );
document.write( "three equations all line up vertically:\r\n" );
document.write( "\r\n" );
document.write( "2x + 3y - 5z = 3\r\n" );
document.write( "1x - 2y + 1z = 0\r\n" );
document.write( "3x + 1y + 3z = 7\r\n" );
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document.write( "Form the determinant D by erasing everything\r\n" );
document.write( "but the coefficients of the letters:\r\n" );
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document.write( "2  + 3  - 5     \r\n" );
document.write( "1  - 2  + 1 \r\n" );
document.write( "3  + 1  + 3     \r\n" );
document.write( "\r\n" );
document.write( "Erase the + signs and move the - signs \r\n" );
document.write( "closer to the numbers:\r\n" );
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document.write( "2    3   -5     \r\n" );
document.write( "1   -2    1 \r\n" );
document.write( "3    1    3\r\n" );
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document.write( "Then put vertical bars around it:\r\n" );
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document.write( "    |2    3   -5|     \r\n" );
document.write( "D = |1   -2    1| \r\n" );
document.write( "    |3    1    3|\r\n" );
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document.write( "Do you know how to find the value of a 3x3 determinant?\r\n" );
document.write( "I'll assume you do and can find that D = -49.\r\n" );
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document.write( "Now we want to find z, which is the 3rd unknown in the\r\n" );
document.write( "system, going left to right.  Since it is the 3rd unknown,\r\n" );
document.write( "we form Dz by replacing the 3rd column of D, which is\r\n" );
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document.write( "-5\r\n" );
document.write( " 1\r\n" );
document.write( " 3\r\n" );
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document.write( "by the column of constants, which is \r\n" );
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document.write( "3\r\n" );
document.write( "0\r\n" );
document.write( "7\r\n" );
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document.write( "getting\r\n" );
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document.write( "     |2    3    3|     \r\n" );
document.write( "Dz = |1   -2    0| \r\n" );
document.write( "     |3    1    7|\r\n" );
document.write( " \r\n" );
document.write( "and we expand that determinant, getting\r\n" );
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document.write( "Dz = -28\r\n" );
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document.write( "        Dz     -28\r\n" );
document.write( "So z = ———— = ————— = \"4%2F7\" \r\n" );
document.write( "         D     -49\r\n" );
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document.write( "----------------------------------------------\r\n" );
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document.write( "Find the value of x in the system of equations\r\n" );
document.write( "2x + y - 4 = 0\r\n" );
document.write( "13x + (5/2)y - 10 = 0\r\n" );
document.write( "using Cramer's rule. (-2,-1,0,1)\r\n" );
document.write( "\r\n" );
document.write( "Write the single letter y as 1y.\r\n" );
document.write( "\r\n" );
document.write( "2x + 1y - 4 = 0\r\n" );
document.write( "13x + (5/2)y - 10 = 0\r\n" );
document.write( "\r\n" );
document.write( "Then get all the letter terms on the left and \r\n" );
document.write( "all the number terms on the right, so that like \r\n" );
document.write( "terms in the three equations all line up \r\n" );
document.write( "vertically:\r\n" );
document.write( "\r\n" );
document.write( " 2x + 1y = 4\r\n" );
document.write( "13x - \"5%2F2\"y = 10\r\n" );
document.write( "\r\n" );
document.write( "Form the determinant D by erasing everything\r\n" );
document.write( "but the coefficients of the letters:\r\n" );
document.write( "\r\n" );
document.write( " 2    1       \r\n" );
document.write( "13  - \"5%2F2\"      \r\n" );
document.write( "\r\n" );
document.write( "Erase the + signs and move the - sign \r\n" );
document.write( "closer to the number:\r\n" );
document.write( "\r\n" );
document.write( " 2   1       \r\n" );
document.write( "13  -\"5%2F2\"\r\n" );
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document.write( "\r\n" );
document.write( "Then put vertical bars around it:\r\n" );
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document.write( "| 2   1|       \r\n" );
document.write( "|13  -\"5%2F2\"|\r\n" );
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document.write( "Do you know how to find the value of a 2x2 determinant?\r\n" );
document.write( "I'll assume you do and can find that D = -18.\r\n" );
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document.write( "Now we want to find x, which is the 1st unknown in the\r\n" );
document.write( "system, going left to right.  Since it is the 1st unknown,\r\n" );
document.write( "we form Dx by replacing the 1st column of D, which is\r\n" );
document.write( "\r\n" );
document.write( " 2\r\n" );
document.write( "13\r\n" );
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document.write( "by the column of constants, which is\r\n" );
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document.write( " 4\r\n" );
document.write( "10\r\n" );
document.write( "\r\n" );
document.write( " getting\r\n" );
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document.write( "Dx = | 4   1|       \r\n" );
document.write( "     |10  -\"5%2F2\"|\r\n" );
document.write( " \r\n" );
document.write( "and we expand that determinant, getting\r\n" );
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document.write( "Dx = -20\r\n" );
document.write( "        Dx     -20\r\n" );
document.write( "So x = ———— = ————— = \"10%2F9\" \r\n" );
document.write( "         D     -18\r\n" );
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document.write( "That's not one of your choices, but it\r\n" );
document.write( "IS correct anyway.  The whole solution\r\n" );
document.write( "is\r\n" );
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document.write( "x = 10/9,  y = 16/9\r\n" );
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document.write( "2x + 1y - 4 = 0\r\n" );
document.write( "13x + \"5%2F2\"y - 10 = 0\r\n" );
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document.write( "2\"10%2F9\" + \"16%2F9\" - 4 = 0\r\n" );
document.write( "13\"10%2F9\" + \"5%2F2\"\"16%2F9\" - 10 = 0\r\n" );
document.write( "\r\n" );
document.write( "\"20%2F9\" + \"80%2F18\" - 4 = 0\r\n" );
document.write( "\"130%2F9\" + \"40%2F9\" - 4 = 0\r\n" );
document.write( "\"210%2F9\"\r\n" );
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document.write( "Find the value of y in the system equations\r\n" );
document.write( "5x - 3y = 18\r\n" );
document.write( "2x + 4y = 2\r\n" );
document.write( "using Cramer's rule. (-2,-1,0,1)\r\n" );
document.write( "\r\n" );
document.write( "Find the value of y in the system of equations\r\n" );
document.write( "2x + 3y - 5z = 3\r\n" );
document.write( "x - 2y + z = 0\r\n" );
document.write( "3x + y + 3z = 7\r\n" );
document.write( "using Cramer's rule \r\n" );
document.write( "(0,4/7,1,10/7)\r\n" );
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