document.write( "Question 400010: I am attempting to solve system of linear equations through elimination. I have an entire list of them due but if you can help me promptly with this one, I should be able to use it as a guide with the others. Thank you in advance.\r
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Algebra.Com's Answer #283231 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Rules:\r\n" );
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document.write( "1.  Pick 2 of the equations, and pick a letter to eliminate, and multiply\r\n" );
document.write( "the equations through as is necessary to make the letter cancel out.\r\n" );
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document.write( "2.  Take the equation you did not use in step 1, together with one of the\r\n" );
document.write( "equations you used in step 1, and eliminate the SAME letter you eliminated\r\n" );
document.write( "in step 1.\r\n" );
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document.write( "3.  The results of step 1 and step 2 give you two equations in two letters.\r\n" );
document.write( "Solve them for the two letters they contain.\r\n" );
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document.write( "4.  Substitute those two values in one of the original equations and solve\r\n" );
document.write( "for the remaining letter (the one you eliminated in steps 1 and 2.\r\n" );
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document.write( "2x - y +  z = 1\r\n" );
document.write( " x + y - 7z = 2\r\n" );
document.write( "3x - y +  z = 0\r\n" );
document.write( "
\r\n" );
document.write( "1.  Pick 2 of the equations, and pick a letter to eliminate, and multiply\r\n" );
document.write( "the equations through as is necessary to make the letter cancel out.\r\n" );
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document.write( "I will pick the 2nd and 3rd equations and pick y to eliminate because that's\r\n" );
document.write( "easy since the y's cancel without multiplying either one through.\r\n" );
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document.write( " x + y - 7z = 2\r\n" );
document.write( "3x - y +  z = 0\r\n" );
document.write( "---------------\r\n" );
document.write( "4x     - 6z = 2\r\n" );
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document.write( "[Notice that since all the numbers in that equation are even, we can\r\n" );
document.write( "divide that equation through by 2.]\r\n" );
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document.write( "2x - 3z = 1  \r\n" );
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\r\n" );
document.write( "2.  Take the equation you did not use in step 1, together with one of the\r\n" );
document.write( "equations you used in step 1, and eliminate the SAME letter you eliminated\r\n" );
document.write( "in step 1.\r\n" );
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document.write( "The equation I did not use in step 1 is\r\n" );
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document.write( "2x - y +  z = 1\r\n" );
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document.write( "I will take it together with this one that I did use in step 1:\r\n" );
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document.write( " x + y - 7z = 2\r\n" );
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document.write( "I will eliminate the letter y because that's the same letter I chose to\r\n" );
document.write( "eliminate in step 1. \r\n" );
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document.write( "I don't need to multiply either equation through by anything because\r\n" );
document.write( "the y's cancel as they are:\r\n" );
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document.write( "2x - y +  z = 1\r\n" );
document.write( " x + y - 7z = 2\r\n" );
document.write( "---------------\r\n" );
document.write( "3x     - 6z = 3\r\n" );
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document.write( "[Notice that since all the numbers in that equation are multiples of 3,\r\n" );
document.write( "we can divide that equation through by 3.]\r\n" );
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document.write( "    x - 2z = 1\r\n" );
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\r\n" );
document.write( "3.  The results of step 1 and step 2 give you two equations in two letters.\r\n" );
document.write( "Solve them for the two letters they contain.\r\n" );
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document.write( "2x - 3z = 1\r\n" );
document.write( " x - 2z = 1\r\n" );
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document.write( "To make the x's cancel multiply the second equation through by -2 and add\r\n" );
document.write( "corresponding terms:\r\n" );
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document.write( " 2x - 3z =  2\r\n" );
document.write( "-2x + 2z = -1\r\n" );
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document.write( "      -z =  1\r\n" );
document.write( "       z = -1\r\n" );
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document.write( "Substitute -1 for z in\r\n" );
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document.write( "   x - 2z =  1\r\n" );
document.write( "x - 2(-1) =  1\r\n" );
document.write( "    x + 2 =  1\r\n" );
document.write( "        x = -1\r\n" );
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document.write( "4.  Substitute those two values in one of the original equations and solve\r\n" );
document.write( "for the remaining letter (the one you eliminated in steps 1 and 2.\r\n" );
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document.write( "So we substitute x = -1 and z = 1 in one of the original equations, say,\r\n" );
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document.write( "    x + y - 7z =  2\r\n" );
document.write( "-1 + y - 7(-1) =  2\r\n" );
document.write( "    -1 + y + 7 =  2\r\n" );
document.write( "         y + 6 =  2\r\n" );
document.write( "             y = -4\r\n" );
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document.write( "So the solution is (x,y,z) = (-1,-4,-1)\r\n" );
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document.write( "Edwin
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