document.write( "Question 904087: Hi would you please help me with this question and could you show me the steps on how to solve it please.\r
\n" ); document.write( "\n" ); document.write( "Solve the system of equations:
\n" ); document.write( "x + y+ z=9
\n" ); document.write( "2x+4y+2z=14
\n" ); document.write( "-x+8y-3z= -39\r
\n" ); document.write( "\n" ); document.write( "My professor said the solution set is {(5,-2,6)} \r
\n" ); document.write( "\n" ); document.write( "Can you kindly show me how he got those answers please. Thanks! \n" ); document.write( "

Algebra.Com's Answer #548516 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You may not have studied the augmented matrix method yet. Here's how to\r\n" );
document.write( "solve it by elimination:\r\n" );
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document.write( "1.  Pick a letter to eliminate.\r\n" );
document.write( "2.  Eliminate that letter from any two of the 3 equations that contain \r\n" );
document.write( "    that letter.\r\n" );
document.write( "3.  Eliminate the SAME letter for one of those equations you just used but\r\n" );
document.write( "    this time using the third equation.\r\n" );
document.write( "4.  Now you have a new system of only two equations in two unknowns.\r\n" );
document.write( "5.  Solve this system for those two unknowns.\r\n" );
document.write( "6.  Substitute those values in one of the original equations to find the\r\n" );
document.write( "    remaining letter.  [It will be the first letter eliminated.    \r\n" );
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document.write( "Add the first and third equations term by term to eliminate x\r\n" );
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document.write( " x +  y +  z =   9\r\n" );
document.write( "-x + 8y - 3z = -39\r\n" );
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document.write( "     9y - 2z = -30\r\n" );
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document.write( "Now eliminate x from the 2nd and 3rd equations\r\n" );
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document.write( " 2x + 4y + 2z =  14\r\n" );
document.write( " -x + 8y - 3z = -39\r\n" );
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document.write( "To make the x's cancel we must multiply the second one\r\n" );
document.write( "above through by 2\r\n" );
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document.write( " 2x +  4y + 2z =  14\r\n" );
document.write( "-2x + 16y - 6z = -78\r\n" );
document.write( "--------------------\r\n" );
document.write( "      20y - 4z = -64\r\n" );
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document.write( "We can simplify that by dividing through by 4\r\n" );
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document.write( "      5y -  z = -16\r\n" );
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document.write( "Now we have this system which is 2 equations and 2 unknowns.\r\n" );
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document.write( "To make the z's cancel we must multiply the second one\r\n" );
document.write( "above through by -2\r\n" );
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document.write( "  9y - 2z = -30\r\n" );
document.write( "-10y + 2z =  32\r\n" );
document.write( "---------------\r\n" );
document.write( "  -y      =   2\r\n" );
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document.write( "Divide both sides by -1\r\n" );
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document.write( "        y = -2\r\n" );
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document.write( "Substitute -2 for y in\r\n" );
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document.write( "      5y -  z = -16\r\n" );
document.write( "    5(-2) - z = -16\r\n" );
document.write( "      -10 - z = -16\r\n" );
document.write( "           -z = -6\r\n" );
document.write( "            z = 6\r\n" );
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document.write( "Substitute both y = -2 and z = 6 in one\r\n" );
document.write( "of the original equations:\r\n" );
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document.write( "    x + y + z = 9 \r\n" );
document.write( " x + (-2) + 6 = 9\r\n" );
document.write( "    x - 2 + 6 = 9\r\n" );
document.write( "        x + 4 = 9\r\n" );
document.write( "            x = 5\r\n" );
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document.write( "Solution (x,y,z) = (5,-2,6)\r\n" );
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document.write( "Edwin

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