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3x+2y+z=8
\n" ); document.write( " 5x-3y+4z=3
\n" ); document.write( " 2x+y+3z=7
\n" ); document.write( ":
\n" ); document.write( "multiply the 2nd equation by -1
\n" ); document.write( " 3x + 2y + z = 8
\n" ); document.write( "-5x + 3y -4z =-3
\n" ); document.write( " 2x+ y + 3z = 7
\n" ); document.write( "------------------addition eliminates x and z
\n" ); document.write( " 0 + 6y + 0 = 12
\n" ); document.write( " y = 12/6
\n" ); document.write( " y = 2
\n" ); document.write( "substituting 2 for y in the 1st equation
\n" ); document.write( "3x + 2(2) + z = 8
\n" ); document.write( "3x + z = 8 - 4
\n" ); document.write( "3x + z = 4
\n" ); document.write( "Do the same on the 3rd equation
\n" ); document.write( "2x + 2 + 3z = 7
\n" ); document.write( "2x + 3z = 7 - 2
\n" ); document.write( "2x + 3z = 5
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st 2 unknown equation by 3, subtract the above equation
\n" ); document.write( "9x + 3z = 12
\n" ); document.write( "2x + 3z = 5
\n" ); document.write( "----------------subtraction eliminates z, find x
\n" ); document.write( "7x + 0 = 7
\n" ); document.write( "x = 1
\n" ); document.write( "Find z using the 2nd original equation
\n" ); document.write( "5x - 3y + 4z = 3
\n" ); document.write( "Replace x and y
\n" ); document.write( "5(1) - 3(2) + 4z = 3
\n" ); document.write( "5 - 6 + 4z = 3
\n" ); document.write( "-1 + 4z = 3
\n" ); document.write( "4z = 3 + 1
\n" ); document.write( "4z = 4
\n" ); document.write( "z = 1
\n" ); document.write( "We have x=1; y=2; z=1
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check in the 2nd original equation 5x - 3y + 4z = 3,
\n" ); document.write( "5(1) - 3(2) + 4(1) = 3
\n" ); document.write( "5 - 6 + 4 = 3\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "