document.write( "Question 334092: solve system of equation by elimination
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Algebra.Com's Answer #239375 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "#1      2x -  y +  z =  7\r\n" );
document.write( "#2      3x + 2y - 2z = -7\r\n" );
document.write( "#3       x - 3y + 4z = 20\r\n" );
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document.write( "All three equations contain all three variables, so\r\n" );
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document.write( "1. Pick a variable to eliminate.  \r\n" );
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document.write( "I'll pick x.\r\n" );
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document.write( "2. Pick two of the equations to eliminate that letter from.\r\n" );
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document.write( "I'll pick #1 & #3\r\n" );
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document.write( "3. Eliminate that variable from them\r\n" );
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document.write( "#1      2x -  y +  z =  7\r\n" );
document.write( "#3       x - 3y + 4z = 20\r\n" );
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document.write( "Multiply #2 through by -2 and add them:\r\n" );
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document.write( "        2x -  y +  z =   7 \r\n" );
document.write( "       -2x + 6y - 8z = -40\r\n" );
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document.write( "             5y - 7z = -33 \r\n" );
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document.write( "4. Pick either one of those equations\r\n" );
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document.write( "I'll pick #3\r\n" );
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document.write( "5. Put it together with the equation you haven't yet used.\r\n" );
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document.write( "I haven't used #2 yet, so I'll put #2 and #3 together:\r\n" );
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document.write( "#2      3x + 2y - 2z = -7\r\n" );
document.write( "#3       x - 3y + 4z = 20\r\n" );
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document.write( "6. Eliminate that same variable from them \r\n" );
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document.write( "Multiply #3 through by -3 and add them:\r\n" );
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document.write( "        3x + 2y +  2z =   9 \r\n" );
document.write( "       -3x + 9y - 12z = -60\r\n" );
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document.write( "            11y - 10z = -51\r\n" );
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document.write( "7.  Put the two equations with the eliminated variable \r\n" );
document.write( "    together as a system of two equations in two variables:\r\n" );
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document.write( "             5y -  7z = -33\r\n" );
document.write( "            11y - 10z = -51 \r\n" );
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document.write( "8.  Solve them for the two variables that they contain.\r\n" );
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document.write( "Eliminate z by mutiplying the first one through by 10,\r\n" );
document.write( "and the second one through by -7\r\n" );
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document.write( "            50y - 70z = -330\r\n" );
document.write( "           -77y + 70z =  357\r\n" );
document.write( "           -----------------\r\n" );
document.write( "           -27y       =   27\r\n" );
document.write( "              y       =   -1\r\n" );
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document.write( "Substitute -1 for y into:    \r\n" );
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document.write( "             5y -  7z = -33\r\n" );
document.write( "           5(-1) - 7z = -33\r\n" );
document.write( "             -5  - 7z = -33\r\n" );
document.write( "                  -7z = -28\r\n" );
document.write( "                    z = 4\r\n" );
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document.write( "9.  Pick one of the original equations to substitute\r\n" );
document.write( "    the two variables you have found in the preceding step.\r\n" );
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document.write( "    I'll pick #3\r\n" );
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document.write( "#3       x - 3y + 4z = 20\r\n" );
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document.write( "10. Substitute and solve for the remaining variable (the first one\r\n" );
document.write( "    picked in step 1.\r\n" );
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document.write( "    I'll substitute y = -1 and z = 4 into #3\r\n" );
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document.write( "         x - 3y + 4z = 20\r\n" );
document.write( "    x - 3(-1) + 4(4) = 20\r\n" );
document.write( "          x + 3 + 16 = 20\r\n" );
document.write( "              x + 19 = 20\r\n" );
document.write( "                   x = 1\r\n" );
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document.write( "So the solution is (x,y,z) = (1,-1,4)\r\n" );
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document.write( "Edwin
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