document.write( "Question 342380: 3. Solve for X, Y, and Z in the following systems of three equations using either substition or elimination methods:
\n" ); document.write( "a. X + 2Y + Z = 22
\n" ); document.write( " X + Y = 15
\n" ); document.write( " 3X + Y + Z = 37
\n" ); document.write( "b. 10X + Y + Z = 603
\n" ); document.write( " 8X + 2Y + Z = 603
\n" ); document.write( " 20X - 10Y - 2Z = -6
\n" ); document.write( "c. 22X + 5Y + 7Z = 12
\n" ); document.write( " 10X + 3Y + 2Z = 5
\n" ); document.write( " 9X + 2Y + 12Z = 14
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Algebra.Com's Answer #245055 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll do the second one only:\r\n" );
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document.write( "10X +   Y +  Z = 603\r\n" );
document.write( " 8X +  2Y +  Z = 603\r\n" );
document.write( "20X - 10Y - 2Z =  -6\r\n" );
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document.write( "Pick any two equations and a letter to eliminate from them.\r\n" );
document.write( "I could pick any two equations and any letter, but you might as\r\n" );
document.write( "well pick the easiest letter to eliminate and the two easiest\r\n" );
document.write( "equations to eliminate it from.  So I will pick the first two\r\n" );
document.write( "equations and eliminate Z from them by multiplying the first one\r\n" );
document.write( "by -1 and adding it to the second equations:\r\n" );
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document.write( "10X +  Y + Z =  603\r\n" );
document.write( "-8X - 2Y - Z = -603\r\n" );
document.write( "-------------------\r\n" );
document.write( " 2X -  Y     =   0\r\n" );
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document.write( "Now use one of those equations with the third equation and eliminate\r\n" );
document.write( "the same letter, Z.  I'll multiply the first original equation by 2\r\n" );
document.write( "and add it to the third equation to make the Z's cancel\r\n" );
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document.write( "16X +  4Y + 2Z = 1206\r\n" );
document.write( "20X - 10Y - 2Z =   -6\r\n" );
document.write( "---------------------\r\n" );
document.write( "36X -  6Y      = 1200\r\n" );
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document.write( "and we can divide that through by 6 to make it easier:\r\n" );
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document.write( "6X - Y = 200\r\n" );
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document.write( "Next we put those two resulting equations together:\r\n" );
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document.write( "2X - Y =   0\r\n" );
document.write( "6X - Y = 200\r\n" );
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document.write( "Multiply the first one of those by -1 so the Y's will cancel:\r\n" );
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document.write( "-2X + Y =   0\r\n" );
document.write( " 6X - Y = 200\r\n" );
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document.write( " 4X     = 200\r\n" );
document.write( "      X = 50\r\n" );
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document.write( "Substitute X = 50 into either one of those equations. I'll\r\n" );
document.write( "pick the first one:\r\n" );
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document.write( "   -2X + Y = 0\r\n" );
document.write( "-2(50) + Y = 0\r\n" );
document.write( "  -100 + Y = 0\r\n" );
document.write( "         Y = 100\r\n" );
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document.write( "Now you have two of the unknowns, so you pick any one\r\n" );
document.write( "of the original three equations and substitute those two\r\n" );
document.write( "values.  I'll pick the second original equation:\r\n" );
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document.write( "      8X +  2Y  + Z = 603\r\n" );
document.write( " 8(50) + 2(100) + Z = 603\r\n" );
document.write( "      400 + 200 + Z = 603\r\n" );
document.write( "            600 + Z = 603\r\n" );
document.write( "                  Z = 3\r\n" );
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document.write( "(X,Y,Z,) = (50,100,3)\r\n" );
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document.write( "Edwin
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