document.write( "Question 20131: Linear Systems\r
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Algebra.Com's Answer #9718 by AnlytcPhil(1806) $\"\"$ $\"About$
You can put this solution on YOUR website!
w + 2x + 3y - 4z = -5
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document.write( "2w -  x +  y - 2z = -7
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document.write( "3w -  x - 2y +  z =  7
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document.write( "4w - 4x - 2y + 3z =  3
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document.write( "Get it in row echelon form. That is, this form:
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document.write( " w + 2x + 3y - 4z = -5
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document.write( "     Ax + By + Cz =  D
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document.write( "          Ey + Fz =  G
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document.write( "               Hz =  I
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document.write( " w + 2x + 3y - 4z = -5
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document.write( "2w -  x +  y - 2z = -7
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document.write( "3w -  x - 2y +  z =  7
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document.write( "4w - 4x - 2y + 3z =  3
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document.write( "Get rid of the 2w by adding -2 times the first equation
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document.write( "to it, and replacing it by what you get
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document.write( " w + 2x + 3y - 4z = -5
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document.write( "   - 5x - 5y + 6z =  3
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document.write( "3w -  x - 2y +  z =  7
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document.write( "4w - 4x - 2y + 3z =  3
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document.write( "Get rid of the 3w by adding -3 times the first equation 
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document.write( "to it, and replacing it by what you get
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document.write( " w + 2x +  3y -  4z =  -5
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document.write( "   - 5x -  5y +  6z =   3
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document.write( "   - 7x - 11y + 13z =  22
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document.write( "4w - 4x -  2y +  3z =   3
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document.write( "Get rid of the 4w by adding -4 times the first equation 
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document.write( "to it, and replacing it by what you get
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document.write( " w +  2x +  3y -  4z =  -5
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document.write( "     -5x -  5y +  6z =   3
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document.write( "     -7x - 11y + 13z =  22
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document.write( "    -12x - 14y + 19z =  23
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document.write( "Get rid of the -7x by adding  -7 times the second equation, or
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document.write( "35x + 35y - 42z = -21, to 5 times the third equation, which is
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document.write( "-35x - 55y + 65z = 110, getting -20y + 23z = 89, and replacing
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document.write( "the third equation by it.
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document.write( " w +  2x +  3y -  4z =  -5
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document.write( "     -5x -  5y +  6z =   3
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document.write( "          -20y + 23z =  89 
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document.write( "    -12x - 14y + 19z =  23
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document.write( "Get rid of the -12x by adding  -12 times the second equation, or
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document.write( "60x + 60y - 72z = -36 to 5 times the fourthion, which is
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document.write( "-60x - 70y + 95z = 115, getting -10y + 23z = 79, and replacing the 
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document.write( "third equation by it
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document.write( "`
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document.write( " w +  2x +  3y -  4z =  -5
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document.write( "     -5x -  5y +  6z =   3
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document.write( "          -20y + 23z =  89 
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document.write( "          -10y + 23z =  79
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document.write( "Get rid of the -10y by adding -1 times the third equation, which is
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document.write( "20y - 23z = -89 to 2 times the fourth equation, which is
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document.write( "-20y + 46z = 158, getting 23z = 69, and replacing the third equation
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document.write( "by it.
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document.write( " w +  2x +  3y -  4z =  -5
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document.write( "     -5x -  5y +  6z =   3
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document.write( "          -20y + 23z =  89 
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document.write( "                 23z =  69 
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document.write( "To finish, 
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document.write( "(1) Solve the 4th equation for z,
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document.write( "(2) Substitute this value of z into the 3rd equation and solve for y
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document.write( "(3) Substitute the values for x and y into the 2nd equation and solve for x
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document.write( "(4) Substitute the values for z, y, and x in the 1st equation to find w.
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document.write( "Answer (w, x, y, z) = (2, 4, -1, 3)
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document.write( "Edwin McCravy
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document.write( "AnlytcPhil@aol.com  
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