document.write( "Question 533806: Solve this system of equation:\r
\n" ); document.write( "\n" ); document.write( "2x + 4y - 3z = -8
\n" ); document.write( "3y + 2z + 6x = 3
\n" ); document.write( "4z - 8x - 7y = 5
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Algebra.Com's Answer #351170 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "2x + 4y - 3z = -8\r\n" );
document.write( "3y + 2z + 6x =  3\r\n" );
document.write( "4z - 8x - 7y =  5\r\n" );
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document.write( "Rearrange the terms on the left so that the terms are\r\n" );
document.write( "all in alphabetical order with the letters:\r\n" );
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document.write( "(A)      2x + 4y - 3z = -8\r\n" );
document.write( "(B)      6x + 3y + 2z =  3\r\n" );
document.write( "(C)     -8x - 7y + 4z =  5\r\n" );
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document.write( "Pick a letter to eliminate and two of the equations to\r\n" );
document.write( "eliminate it from:\r\n" );
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document.write( "I will pick the letter x to eliminate and I will pick\r\n" );
document.write( "(A) and (B) to eliminate it from:\r\n" );
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document.write( "I will multiply (A) by -3 and add (B) to it\r\n" );
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document.write( "        -6x - 12y +  9z = 24\r\n" );
document.write( "(B)      6x +  3y +  2z =  3\r\n" );
document.write( "------------------------------\r\n" );
document.write( "(D)           -9y + 11z = 27\r\n" );
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document.write( "Eliminate the SAME letter from a different pair of equations,\r\n" );
document.write( "[that is, you will choose the equation you did not choose before\r\n" );
document.write( "along with one of the equations that you did choose before.]\r\n" );
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document.write( "I will pick (A) and (C) to eliminate the SAME letter x from:\r\n" );
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document.write( "I will multiply (A) by 4 and add (C) to it\r\n" );
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document.write( "         8x + 16y - 12z = -32\r\n" );
document.write( "(C)     -8x -  7y +  4z =   5\r\n" );
document.write( "-------------------------------\r\n" );
document.write( "(E)            9y -  8z = -27\r\n" );
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document.write( "Now we have reduced the 3 equations and 3 unknowns down\r\n" );
document.write( "to just 2 equations (D) and (E) and 2 unknowns:\r\n" );
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document.write( "(D)          -9y + 11z =  27\r\n" );
document.write( "(E)           9y -  8z = -27\r\n" );
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document.write( "The y's will eliminate by just adding them as they are:\r\n" );
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document.write( "(D)          -9y + 11z =  27\r\n" );
document.write( "(E)           9y -  8z = -27\r\n" );
document.write( "------------------------------\r\n" );
document.write( "                    3z = 0\r\n" );
document.write( "                     z = \r\n" );
document.write( "                     z = 0\r\n" );
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document.write( "Substitute z = 0 in (E)\r\n" );
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document.write( "            9y -  8(0) = -27\r\n" );
document.write( "                9y - 0 = -27\r\n" );
document.write( "                    9y = -27\r\n" );
document.write( "                     y = -3\r\n" );
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document.write( "Substitute y = -3 and z = 0 into one of the originals.\r\n" );
document.write( "I'll pick (A)\r\n" );
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document.write( "(A)      2x + 4y - 3z = -8\r\n" );
document.write( "    2x + 4(-3) - 3(0) = -8\r\n" );
document.write( "          2x - 12 - 0 = -8\r\n" );
document.write( "              2x - 12 = -8\r\n" );
document.write( "                   2x =  4\r\n" );
document.write( "                    x =  2\r\n" );
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document.write( "Solution: (x,y,z) = (2,-3,0)\r\n" );
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document.write( "Edwin

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