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The equations to be solved are:\r
\n" ); document.write( "\n" ); document.write( "x + y + z = -3 _____(1)
\n" ); document.write( "2x + 5y + 2z = -12 ____(2)
\n" ); document.write( "-x + 9y - 3z = -11 ____(3)\r
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\n" ); document.write( "\n" ); document.write( "To solve 3 simultaneous equations in 3 unknowns our objective should be to eliminate any one unknown in order to obtain 2 simultaneous equations in 2 unknowns. To achieve this end, here, we shall eliminate 'x' between all the 3 equations.\r
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\n" ); document.write( "\n" ); document.write( "Substituting the value of 'x' from (1) in (2) eliminates 'x' between (1) and (2) thus giving the new equation
\n" ); document.write( "2(-3 - y - z) + 5y + 2z = -12
\n" ); document.write( "or -6 - 2y - 2z + 5y + 2z = -12
\n" ); document.write( "or 3y = -12 + 6 = -6
\n" ); document.write( "or y = -6/3 = -2 _________(4)\r
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\n" ); document.write( "\n" ); document.write( "Adding (1) and (3) eliminates 'x' between (1) and (3) thus giving the new equation
\n" ); document.write( "(y + z) + (9y - 3z) = -3 + (-11)
\n" ); document.write( "or 10y - 2z = -14
\n" ); document.write( "or 5y - z = -7 [dividing both sides by 2]
\n" ); document.write( "or z = 5y + 7 __________(5)\r
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\n" ); document.write( "\n" ); document.write( "Substituting the value of 'y' from (4) in (5) we get the value of 'z'
\n" ); document.write( "z = 5(-2) + 7 = -10 + 7 = -3\r
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\n" ); document.write( "\n" ); document.write( "Putting y = -2 and z = -3 in (1) we have
\n" ); document.write( "x - 2 - 3 = -3
\n" ); document.write( "or x = 2\r
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\n" ); document.write( "\n" ); document.write( "Thus, the reqd. solution is x = 2, y = -2 and z = -3. \n" ); document.write( "