document.write( "Question 370426: I must solve this system if possible, I worked the system and received the answer below...Im wondering if it is correct.\r
\n" ); document.write( "\n" ); document.write( "3x+y+z=0
\n" ); document.write( "2x-y+z=0
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\n" ); document.write( "\n" ); document.write( "My answer is \r
\n" ); document.write( "\n" ); document.write( "z=4, y=-25, x=18\r
\n" ); document.write( "\n" ); document.write( "Thank U in advance. \n" ); document.write( "

Algebra.Com's Answer #264037 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "z=4, y=-25, x=18 \r\n" );
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document.write( "These do not check in the first equation\r\n" );
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document.write( "  3x  +   y   +  z = 0\r\n" );
document.write( "3(18) + (-25) +  4 = 0\r\n" );
document.write( "  54  -   25  +  4 = 0\r\n" );
document.write( "                33 = 0\r\n" );
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document.write( "These do not check in the second equation, either.\r\n" );
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document.write( "  2x  -    y  +  z = 0\r\n" );
document.write( "2(18) - (-25) +  4 = 0\r\n" );
document.write( "  36  +   25  +  4 = 0\r\n" );
document.write( "                65 = 0\r\n" );
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document.write( "These do not check in the third equation, either.\r\n" );
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document.write( "  2x  +    y  +  z = 0\r\n" );
document.write( "2(18) + (-25) +  4 = 0\r\n" );
document.write( "  36  -   25  +  4 = 0\r\n" );
document.write( "                15 = 0\r\n" );
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document.write( "The only solution is x=0, y=0, z=0\r\n" );
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document.write( "The other tutor is right in one respect, but wrong in another respect.\r\n" );
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document.write( "When the numbers on the right (not coefficients, as he stated) are all\r\n" );
document.write( "aero, it's true that x = y = z = 0 is a solution.  However that is not\r\n" );
document.write( "necessarily the only solution.  It was in your case, but not in all\r\n" );
document.write( "cases.\r\n" );
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document.write( "For example:\r\n" );
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document.write( "x +  y + 3z = 0\r\n" );
document.write( "x + 2y + 4z = 0\r\n" );
document.write( "x + 3y + 5z = 0\r\n" );
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document.write( "This one has infinitely many solutions.\r\n" );
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document.write( "x = y = z = 0  is indeed a solution, but also\r\n" );
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document.write( "x=-2, y=-1, and z=1 is a solution and\r\n" );
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document.write( "x=4, y=2, and z=-2 is also a solution.\r\n" );
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document.write( "The general solution is\r\n" );
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document.write( "x = -2k, y = -k, and z = k, where k is any number\r\n" );
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document.write( "Edwin

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