document.write( "Question 1202869: Please help me solve these equations
\n" ); document.write( "1) x + y + z = 3
\n" ); document.write( "x + 2y - z = 2
\n" ); document.write( "x + yz + zx = 3
\n" ); document.write( "2) x +yz = 2
\n" ); document.write( " y + zx = 2
\n" ); document.write( " z + xy = 2 \n" ); document.write( "

Algebra.Com's Answer #838059 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "x + 2y - z = 2\r\n" );
document.write( "x + yz + zx = 3\r\n" );
document.write( "2) x +yz = 2\r\n" );
document.write( "   y + zx = 2\r\n" );
document.write( "   z + xy = 2\r\n" );
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document.write( "I'll do # 1 for you. Apply the same concept and you should have no problems doing # 2.\r\n" );
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document.write( "       x + y + z = 3______x + y = 3 - z --- eq (i)\r\n" );
document.write( "                     x + 2y - z = 2 ------- eq (ii)\r\n" );
document.write( "                    x + yz + xz = 3 ------- eq (iii)\r\n" );
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document.write( "                   2x + 2y + 2z = 6 ----- Multiplying eq (i) by 2 ------ eq (iv)\r\n" );
document.write( "                     x + 2y - z = 2 ----- eq (ii)\r\n" );
document.write( "                         x + 3z = 4 ----- Subtracting eq (ii) from (iv) \r\n" );
document.write( "                              x = 4 - 3z ----- eq (v)\r\n" );
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document.write( "x + yz + xz = 3____x + (y + x)z = 3 --- eq (iii)\r\n" );
document.write( "                   x + (3 - z)z = 3 --- Substituting 3 - z for x + y in eq (iii)\r\n" );
document.write( "                      --- eq (vi)\r\n" );
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document.write( "                  ----- Substituting 4 - 3z for x in eq (vi)\r\n" );
document.write( "                           \r\n" );
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document.write( "                             z = 1\r\n" );
document.write( "                              x = 4 - 3z ------ Substituting 1 for z in eq (v)\r\n" );
document.write( "                              x = 4 - 3(1)\r\n" );
document.write( "                              x = 4\r\n" );
document.write( "                              x = 1\r\n" );
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document.write( "                          x + y = 3 - z\r\n" );
document.write( "                          1 + y = 3 - 1 ------- Substituting 1 for x, and 1 for z in eq (i)\r\n" );
document.write( "                              y = 2\r\n" );
document.write( "                              y = 1\r\n" );
document.write( "                    (x, y, z) = (1, 1, 1)\r\n" );
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document.write( "                             z = - 1\r\n" );
document.write( "                              x = 4 - 3z ------ eq (v)\r\n" );
document.write( "                              x = 4 - 3(- 1) -- Substituting - 1 for z in eq (v)\r\n" );
document.write( "                              x = 4 + 3\r\n" );
document.write( "                              x = 7\r\n" );
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document.write( "                          x + y = 3 - z\r\n" );
document.write( "                          7 + y = 3 - - 1 ----- Substituting 7 for x, and - 1 for z in eq (i)\r\n" );
document.write( "                          7 + y = 4\r\n" );
document.write( "                              y = 4 - 7\r\n" );
document.write( "                              y = - 3\r\n" );
document.write( "                    (x, y, z) = (7, - 3, - 1)\r\n" );
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document.write( "The fact that x, y, and z are purported to have DIFFERENT values would suggest to me that\r\n" );
document.write( "(x, y, z) = (1, 1, 1) is NOT the solution set, but (x, y, z) = (7, - 3, - 1) instead,\r\n" );
document.write( "would be the CORRECT solution set!!\r\n" );
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document.write( "I don't think it has to be stated that x, y, and z are different numbers. The fact that they're \r\n" );
document.write( "given DIIFERENT variables would automatically mean that they are.\r\n" );
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document.write( "I believe, wholeheartedly, that a note should've been attached to this problem, stating that .

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