document.write( "Question 831301: solve the system:
\n" ); document.write( "x1+x2 =5
\n" ); document.write( " x2+x3 =5
\n" ); document.write( " x3+x4=-5
\n" ); document.write( "x1 +x4=-5 \r
\n" ); document.write( "\n" ); document.write( "[x1] = [ ] + [ ]s
\n" ); document.write( "[x2] = [ ] + [ ]s
\n" ); document.write( "[x3] = [ ] + [ ]s
\n" ); document.write( "[x4] = [ ] + [ ]s \n" ); document.write( "
Algebra.Com's Answer #501243 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Put in missing variables with 0 coefficients\r\n" );
document.write( "and give single variables 1 coefficents\r\n" );
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document.write( "Put the coefficients in a 4×5 augmented matrix and do row operations\r\n" );
document.write( "to get 0's below the diagonals:\r\n" );
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document.write( "-1*R1+R4->R4   (Multiply row 1 by -1, add to row 4, put it in row 4.) \r\n" );
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document.write( "R2+R4->R4    (Add row 2 and R4 and put it in row 4)  \r\n" );
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document.write( "-R3+R4->R4\r\n" );
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document.write( "Eliminate the 0s and 1 coefficients, which\r\n" );
document.write( "means we eliminate the entire bottom equation. \r\n" );
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document.write( "We let \"x%5B4%5D=s\"\r\n" );
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document.write( "Solve the bottom equation of the system: \"x%5B3%5D=-5-s\"\r\n" );
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document.write( "Substitute in the middle equation and solve:\r\n" );
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document.write( "\"x%5B2%5D%2Bx%5B3%5D+=+5\"\r\n" );
document.write( "\"x%5B2%5D%2B%28-5-s%29+=+5\"\r\n" );
document.write( "{{x[2]-5-s = 5}}}\r\n" );
document.write( "{{x[2]= 10+s}}}\r\n" );
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document.write( "Substitute in the top equation\r\n" );
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document.write( "\"x%5B1%5D%2Bx%5B2%5D+=+5\"\r\n" );
document.write( "\"x%5B1%5D%2B%2810%2Bs%29+=+5\"\r\n" );
document.write( "\"x%5B1%5D%2B10%2Bs+=+5\"\r\n" );
document.write( "\"x%5B1%5D=-5-s\"\r\n" );
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document.write( "\"x%5B1%5D=-5-s\"\r\n" );
document.write( "\"x%5B2%5D=+10%2Bs\"\r\n" );
document.write( "\"x%5B3%5D=-5-s\"\r\n" );
document.write( "\"x%5B4%5D=s\"\r\n" );
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document.write( "or in the form that you gave:\r\n" );
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document.write( "[x1] = [5] + [-1]s \r\n" );
document.write( "[x2] = [10] + [1]s\r\n" );
document.write( "[x3] = [-5] + [-1]s \r\n" );
document.write( "[x4] = [0] + [1]s\r\n" );
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document.write( "Edwin
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