document.write( "Question 20130: Linear Systems\r
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Algebra.Com's Answer #9717 by AnlytcPhil(1806) $\"\"$ $\"About$

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2x + 3y -  z = 1
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document.write( " x -  y -  z = 2
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document.write( "3x + 2y - 3z = 3
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document.write( "Get it in echelon form
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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( "2x + 3y -  z = 1
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document.write( " x -  y -  z = 2
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document.write( "3x + 2y - 3z = 3
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document.write( "Get rid of the x in the 2nd equation by multiplying it by -2,
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document.write( "getting -2x + 2y + 2z = -4, and adding 1 times the first equation to it,
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document.write( "getting  5y + z = -3.  Replace the second equation with this one
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document.write( "2x + 3y -  z =  1
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document.write( "     5y +  z - -3 
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document.write( "3x + 2y - 3z =  3
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document.write( "Get rid of the 3x in the 3rd equation by multiplying it by 2,
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document.write( "getting 6x + 4y - 6z = 6, and adding -3 times the first equation to it,
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document.write( "namely -6x - 9y + 3z = -3, getting  -5y - 3z = 3.  Replace the third equation
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document.write( "with this one
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document.write( "2x + 3y -  z =  1
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document.write( "     5y +  z = -3 
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document.write( "    -5y - 3z =  3
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document.write( "Get rid of the -5y in the 3rd equation by multiplying it by 1,
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document.write( "and adding 1 times the second equation to it, getting  -2z = 0
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document.write( "Replace the third equation with this one
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document.write( "2x + 3y -  z =  1
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document.write( "     5y +  z = -3 
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document.write( "         -2z =  0
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document.write( "Finish by:
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document.write( "(1) solving the third equation for z
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document.write( "(2) Substitute the value you got for z into the second equation, and 
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document.write( "solve for y   
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document.write( "(3) Substitute the values of z and y into the first equation and solve 
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document.write( "for x.  Answer (x, y, z) = (7/5, -3/5, 0)\r
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document.write( "Edwin 
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