document.write( "Question 360587: Solve the system of equations. How do I solve one of the equations for one variable then substitute the solution back into the other 2 equations?
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document.write( " 4x - 4y -  z = 38\r\n" );
document.write( "  x + 4y - 3z =  6\r\n" );
document.write( "-3x + 2y -  z = -14\r\n" );
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Algebra.Com's Answer #257305 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)    4x - 4y -  z =  38\r\n" );
document.write( "(2)     x + 4y - 3z =   6\r\n" );
document.write( "(3)   -3x + 2y -  z = -14\r\n" );
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document.write( "Pick any one of the three equations and pick one of the variables in it to solve for.\r\n" );
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document.write( "I'll pick equation (2) and pick x to solve for:\r\n" );
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document.write( "(2)     x + 4y - 3z = 6\r\n" );
document.write( "(4)               x = 6 - 4y + 3z\r\n" );
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document.write( "Now substitute 6 - 4y + 3z for x in the other two equations:\r\n" );
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document.write( "Substituting 6 - 4y + 3z for x in equation (1) and simplifying:\r\n" );
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document.write( "(1)                4x - 4y - z = 38\r\n" );
document.write( "       4(6 - 4y + 3z) - 4y - z = 38 \r\n" );
document.write( "       24 - 16y + 12z - 4y - z = 38\r\n" );
document.write( "                24 - 20y + 11z = 38\r\n" );
document.write( "(5)                 -20y + 11z = 14\r\n" );
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document.write( "Substituting 6 - 4y + 3z for x in equation (3) and simplifying:\r\n" );
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document.write( "(3)   -3x + 2y -  z = -14\r\n" );
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document.write( "(1)               -3x + 2y - z = -14\r\n" );
document.write( "      -3(6 - 4y + 3z) + 2y - z = -14 \r\n" );
document.write( "       -18 + 12y - 9z + 2y - z = -14\r\n" );
document.write( "               -18 + 14y - 10z = -14\r\n" );
document.write( "(6)                  14y - 10z = 4\r\n" );
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document.write( "Now we put equations (5) and (6) together as a system of two\r\n" );
document.write( "equations and 2 variables:\r\n" );
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document.write( "(5)                 -20y + 11z = 14\r\n" );
document.write( "(6)                  14y - 10z =  4\r\n" );
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document.write( "It's too hard to do that by substitution, so I'll use elimination:\r\n" );
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document.write( "To eliminate z, multiply equation (5) through by 10, and equation (6) \r\n" );
document.write( "through by 11, and add the resulting equations term by term:\r\n" );
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document.write( "                  -200y + 110z = 140\r\n" );
document.write( "                   154y - 110z =  44\r\n" );
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document.write( "                   -46y        = 184\r\n" );
document.write( "(7)                          y = -4\r\n" );
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document.write( "Substituting in equation (6)\r\n" );
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document.write( "(6)                  14y - 10z =  4\r\n" );
document.write( "                  14(-4) - 10z =  4\r\n" );
document.write( "                     -56 - 10z =  4\r\n" );
document.write( "                          -10z = 60 \r\n" );
document.write( "(8)                          z = -6\r\n" );
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document.write( "Now we substitute for y amd z from equations (7) and (8) into equation (4)\r\n" );
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document.write( "(4)               x = 6 - 4y + 3z\r\n" );
document.write( "                  x = 6 - 4(-4) + 3(-6)\r\n" );
document.write( "                  x = 6 + 16 - 18\r\n" );
document.write( "                  x = 4\r\n" );
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document.write( "Edwin

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