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(1) 2w + x - 3y + 0 = 19
\n" ); document.write( "(2) 3w - x - 3y - 2z = 14
\n" ); document.write( "(3) w - 2w - y - 2z = -2
\n" ); document.write( "(4)-2w + 2x + 3y + z = -7
\n" ); document.write( "To solve, the simplist method (used by most computer algorithms) is elimination.\r
\n" ); document.write( "\n" ); document.write( "Using (3) as the \"anchor\" polynomial we can eliminate w in each of the other three by performing the following operations;
\n" ); document.write( "(1) - 2*(3) yields (5) 5x - y + 4z = 23
\n" ); document.write( "(2) - 3*(3) yields (6) 5x + 4z = 20
\n" ); document.write( "(4) + 2*(3) yields (7)-2x + y - 3z = -11\r
\n" ); document.write( "\n" ); document.write( "Substituting (6) into (5) yields the value of the variable y;
\n" ); document.write( " y = -3
\n" ); document.write( "Now let y = -3 in (7) to result with
\n" ); document.write( "(7)' -2x - 3z = -8
\n" ); document.write( "Using (7)' and (6) we have
\n" ); document.write( " -2x - 3z = -8 and
\n" ); document.write( " 5x + 4z = 20
\n" ); document.write( "The simultation solution of this pair is
\n" ); document.write( " x = 4
\n" ); document.write( " z = 0
\n" ); document.write( "Substitute the derived values of x, y, and z into (1) yields
\n" ); document.write( " 2w + 4 - 3*(-3) = 19
\n" ); document.write( " 2w = 6
\n" ); document.write( " w = 3
\n" ); document.write( "Are the values correct?
\n" ); document.write( "Substitute each into the four given equations and see if we get equality.
\n" ); document.write( "Is (6+4+9+0=19? yes
\n" ); document.write( "Is (9-4+9+0=14)? Yes
\n" ); document.write( "Is (3-8+3+0=-2)? Yes
\n" ); document.write( "Is (-6+8-9+0=-7)? Yes\r
\n" ); document.write( "\n" ); document.write( "The answer is w = 3, x = 4, y = -3 and z = 0
\n" ); document.write( " \n" ); document.write( "