document.write( "Question 354992: I am supposed to solve the systems of equation in three variables. \r
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\n" ); document.write( "7x+3y+4z=29 \n" ); document.write( "

Algebra.Com's Answer #253726 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Equation (1):     5x+2y = 4\r\n" );
document.write( "Equation (2):     3x+4y+2z = 6\r\n" );
document.write( "Equation (3):     7x+3y+4z = 29\r\n" );
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document.write( "Since z is already eliminated in the equation (1), we\r\n" );
document.write( "eliminate z from equations (2) and (3) by multiplying\r\n" );
document.write( "equation (2) through by -2 getting\r\n" );
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document.write( "                 -6x-8y-4z = -12\r\n" );
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document.write( "and adding it to equation (3):\r\n" );
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document.write( "                  7x+3y+4z =  29\r\n" );
document.write( "                 -6x-8y-4z = -12\r\n" );
document.write( "                 ---------------\r\n" );
document.write( "Equation (4)       x-5y    =  17\r\n" );
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document.write( "Now we take equation (1) with equation (4):\r\n" );
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document.write( "Equation (1):     5x+2y =  4\r\n" );
document.write( "Equation (4)       x-5y = 17\r\n" );
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document.write( "Solve equation (4) for x:\r\n" );
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document.write( "Equation (5)          x = 17+5y\r\n" );
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document.write( "and substitute 17+5y for x in equation (1)\r\n" );
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document.write( "            5(17+5y)+2y = 4\r\n" );
document.write( "              85+25y+2y = 4\r\n" );
document.write( "                 85+27y = 4\r\n" );
document.write( "                    27y = 4-85\r\n" );
document.write( "                    27y = -81\r\n" );
document.write( "                      y = -3\r\n" );
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document.write( "Substituting that in equation (5):\r\n" );
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document.write( "                      x = 17+5y\r\n" );
document.write( "                      x = 17+5(-3)\r\n" );
document.write( "                      x = 17-15\r\n" );
document.write( "                      x = 2\r\n" );
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document.write( "Substitute x = 2 and y = -3 in equation (2)\r\n" );
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document.write( "               3x+4y+2z = 6\r\n" );
document.write( "          3(2)+4(-3)+2z = 6\r\n" );
document.write( "                6-12+2z = 6\r\n" );
document.write( "                  -6+2z = 6\r\n" );
document.write( "                     2z = 12\r\n" );
document.write( "                      z = 6\r\n" );
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document.write( "So the solution is , , \r\n" );
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document.write( "Edwin

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