document.write( "Question 747669: Solve the following system of equation
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\n" ); document.write( " x–3y+3z = 10
\n" ); document.write( "2x+ y–3z = –3
\n" ); document.write( " x–2y+ z = 6 \n" ); document.write( "
Algebra.Com's Answer #455069 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x–3y+3z = 10\r\n" );
document.write( "2x+ y–3z = –3\r\n" );
document.write( " x–2y+ z =  6\r\n" );
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document.write( "Add the first two equations above\r\n" );
document.write( "term by term and the x's will\r\n" );
document.write( "cancel:\r\n" );
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document.write( " x–3y+3z = 10\r\n" );
document.write( "2x+ y–3z = –3\r\n" );
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document.write( "3x-2y    =  7\r\n" );
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document.write( "That has z eliminated. So we \r\n" );
document.write( "eliminate z from the 2nd and\r\n" );
document.write( "3rd equations at the top:\r\n" );
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document.write( " x–3y+3z = 10\r\n" );
document.write( " x–2y+ z =  6\r\n" );
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document.write( "We need to multiply x-2y+z=6\r\n" );
document.write( "through by -3 to make the\r\n" );
document.write( "z's cancel when we add them \r\n" );
document.write( "term by term:\r\n" );
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document.write( "  x–3y+3z =  10\r\n" );
document.write( "-3x+6y-3z = -18\r\n" );
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document.write( "-2x+3y    =  -8\r\n" );
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document.write( "So we have a system of only\r\n" );
document.write( "two equations in two unknowns:\r\n" );
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document.write( " 3x-2y =  7\r\n" );
document.write( "-2x+3y = -8\r\n" );
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document.write( "To make the y's cancel multiply\r\n" );
document.write( "the first one by 3 and the second \r\n" );
document.write( "one through by 2\r\n" );
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document.write( " 9x-6y =  21\r\n" );
document.write( "-4x+6y = -16\r\n" );
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document.write( " 5x    =   5\r\n" );
document.write( "     x = 1\r\n" );
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document.write( "Substitute x = 1 in\r\n" );
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document.write( "  3x-2y = 7\r\n" );
document.write( "3(1)-2y = 7   \r\n" );
document.write( "   3-2y = 7\r\n" );
document.write( "    -2y = 4\r\n" );
document.write( "      y = -2\r\n" );
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document.write( "Substitute x = 1 and y = -2 in one\r\n" );
document.write( "of the original equations to find\r\n" );
document.write( "z.\r\n" );
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document.write( "     x–3y+3z = 10\r\n" );
document.write( "(1)-3(-2)+3z = 10\r\n" );
document.write( "  1 + 6 + 3z = 10\r\n" );
document.write( "      7 + 3z = 10\r\n" );
document.write( "          3z = 3\r\n" );
document.write( "           z = 1\r\n" );
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document.write( "Solution (x,y,z) = (1,-2,1)\r\n" );
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document.write( "Edwin
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