document.write( "Question 1025140: Which ordered triple represents all of the solutions to the system of equations shown below?\r
\n" ); document.write( "\n" ); document.write( "2x ­- 2y ­- z = 6
\n" ); document.write( "-x + y + 3z = -­3
\n" ); document.write( "3x ­- 3y + 2z = 9\r
\n" ); document.write( "\n" ); document.write( "A.) (­-x, x + 2, 0)
\n" ); document.write( "B.) (x, x ­- 3, 0)
\n" ); document.write( "C.) (x + 2, x, 0)
\n" ); document.write( "D.) (0, y, y + 4)\r
\n" ); document.write( "\n" ); document.write( "Struggling a bit with this one. \n" ); document.write( "
Algebra.Com's Answer #640452 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "This is a mean problem because it would take lots\r\n" );
document.write( "of solving and switching variables around to find\r\n" );
document.write( "the solution, in all the different forms in the \r\n" );
document.write( "choices.\r\n" );
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document.write( "So what I would do in a case like this is pick a \r\n" );
document.write( "random value for x in the first 3 answers and for \r\n" );
document.write( "y in the 4th answer, and try to eliminate the wrong \r\n" );
document.write( "ones:\r\n" );
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document.write( "A.) (­-x, x + 2, 0)\r\n" );
document.write( "B.) (x, x ­- 3, 0)\r\n" );
document.write( "C.) (x + 2, x, 0)\r\n" );
document.write( "D.) (0, y, y + 4) \r\n" );
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document.write( "Pick 1 for x and y, and you get:\r\n" );
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document.write( "A.) (­-1, 3, 0)\r\n" );
document.write( "B.) (1, -2, 0)\r\n" );
document.write( "C.) (3, 1, 0)\r\n" );
document.write( "D.) (0, 1, 5)\r\n" );
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document.write( "2x ­- 2y ­- z = 6 \r\n" );
document.write( "-x + y + 3z = -­3 \r\n" );
document.write( "3x ­- 3y + 2z = 9\r\n" );
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document.write( "try A.)   Substitute (x,y,z) =(-1,3,0)\r\n" );
document.write( "in the first equation:\r\n" );
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document.write( "2(-1) ­- 2(3) ­- (-1) = 6\r\n" );
document.write( "             -2-6+1 = 6\r\n" );
document.write( "                 -7 = 6\r\n" );
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document.write( "That doesn't check in the first equation.\r\n" );
document.write( "So (A) is eliminated\r\n" );
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document.write( "try B.)   (x,y,z) =(1,-2,0)\r\n" );
document.write( "in the first equation:\r\n" );
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document.write( "2(1) ­- 2(-2) ­- (0) = 6\r\n" );
document.write( "             2+4-0 = 6\r\n" );
document.write( "                 6 = 6\r\n" );
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document.write( "That checks in the first equation.  So (B) might be\r\n" );
document.write( "the correct choice.  But let's check (C) and (D)\r\n" );
document.write( "before we make the decision that (B) is the correct.\r\n" );
document.write( "For it might not check in the other two equations.\r\n" );
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document.write( "try C.)   (x,y,z) =(3,1,0)\r\n" );
document.write( "in the first equation:\r\n" );
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document.write( "2(3) ­- 2(1) ­- (0) = 6\r\n" );
document.write( "             6-2-0 = 6\r\n" );
document.write( "                 4 = 6\r\n" );
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document.write( "That doesn't check in the first equation.\r\n" );
document.write( "So C.) is eliminated\r\n" );
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document.write( "try D.) (x,y,z) =(0,1,5)\r\n" );
document.write( "in the first equation:\r\n" );
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document.write( "2(0) ­- 2(1) ­- (5) = 6\r\n" );
document.write( "             0-2-5 = 6\r\n" );
document.write( "                -7 = 6\r\n" );
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document.write( "That doesn't check in the first equation.\r\n" );
document.write( "So D.) is eliminated\r\n" );
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document.write( "So the correct choice can only be B.)\r\n" );
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document.write( "Some teachers may frown on this method.  But\r\n" );
document.write( "it is often the easiest way when you have a\r\n" );
document.write( "multiple choice test like this, and it would\r\n" );
document.write( "take a long time to solve in every form.\r\n" );
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document.write( "Edwin
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