document.write( "Question 306408: Use Gaussian elimination to solve the system\r
\n" ); document.write( "\n" ); document.write( "w + z = 380
\n" ); document.write( "w + x = 600
\n" ); document.write( "x - y = 170
\n" ); document.write( "y - z = 50\r
\n" ); document.write( "\n" ); document.write( "The solution set is {_,_,_} \n" ); document.write( "

Algebra.Com's Answer #219296 by JBarnum(2146) $\"\"$ $\"About$

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w + z = 380
\n" ); document.write( "w + x = 600
\n" ); document.write( "x - y = 170
\n" ); document.write( "y - z = 50\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "id start working backwards
\n" ); document.write( " $\"y-z=50\"$ solve for y
\n" ); document.write( " $\"highlight%28y=z%2B50%29\"$
\n" ); document.write( " $\"x-y=170\"$ solve for x
\n" ); document.write( " $\"x=170%2By\"$ fill in y with what it equals
\n" ); document.write( " $\"x=170%2B%28z%2B50%29\"$
\n" ); document.write( " $\"highlight%28x=220%2Bz%29\"$
\n" ); document.write( " $\"w%2Bx=600\"$ solve for w
\n" ); document.write( " $\"w=600-x\"$ substitute for x
\n" ); document.write( " $\"w=600-%28220%2Bz%29\"$
\n" ); document.write( " $\"highlight%28w=380%2Bz%29\"$
\n" ); document.write( " $\"w%2Bz=380\"$ solve for z
\n" ); document.write( " $\"z=380-w\"$ substitute for w
\n" ); document.write( " $\"z=380-%28380%2Bz%29\"$
\n" ); document.write( " $\"0=0\"$
\n" ); document.write( "so z can be any number
\n" ); document.write( "so if z=1 then x=221 y=51 w=381
\n" ); document.write( "if z=2 then x=222 y=52 w=382
\n" ); document.write( "if z=3 then x=223 y=53 w=383
\n" ); document.write( "and so on
\n" ); document.write( "{z=|(-∞,+∞)}
\n" ); document.write( "all real numbers \n" ); document.write( "

\n" );