document.write( "Question 876837: Solve: 2x + 3y + 4z = 20, x + y + 2z = 9, 3x + 2y + z = 10 \n" ); document.write( "

Algebra.Com's Answer #529129 by mananth(16946) $\"\"$ $\"About$

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2 x + 3 y + 4 z = 20 -------------- 1
\n" ); document.write( "1 x + 1 y 2 z = 9 -------------- 2
\n" ); document.write( "3 x + 2 y + 1 z = 10 -------------- 3
\n" ); document.write( "
\n" ); document.write( "consider equation 1 &2 Eliminate y
\n" ); document.write( "Multiply 1 by -1 -5
\n" ); document.write( "Multiply 2 by 3 4
\n" ); document.write( "we get
\n" ); document.write( "-2 x + -3 y + -4 z = -20
\n" ); document.write( "3 x + 3 y + 6 z = 27
\n" ); document.write( "Add the two
\n" ); document.write( "1 x + 0 y + 2 z = 7 ------------- 4
\n" ); document.write( "consider equation 2 & 3 Eliminate y
\n" ); document.write( "Multiply 2 by -2
\n" ); document.write( "Multiply 3 by 1
\n" ); document.write( "we get
\n" ); document.write( "-2 x + -2 y + -4 z = -18
\n" ); document.write( "3 x + 2 y + 1 z = 10
\n" ); document.write( "Add the two
\n" ); document.write( "1 x + 0 y + -3 z = -8 -------------5 5
\n" ); document.write( "Consider (4) & (5) Eliminate x
\n" ); document.write( "Multiply 4 by -1
\n" ); document.write( "Multiply (5) by 1
\n" ); document.write( "we get
\n" ); document.write( "-1 x + -2 z = -7
\n" ); document.write( "1 x + -3 z = -8
\n" ); document.write( "Add the two
\n" ); document.write( "0 x + -5 z = -15
\n" ); document.write( "/ -5
\n" ); document.write( "z = 3
\n" ); document.write( "1 x + -3 z= -8
\n" ); document.write( "1 x + -9 = -8
\n" ); document.write( " x = 1
\n" ); document.write( "Plug x & z in eq (1)
\n" ); document.write( "2 x + 3 y + 4 z = 20 -------------- 1
\n" ); document.write( " 2 + 3 y + 12 = 20
\n" ); document.write( " 3 y = 6
\n" ); document.write( " y = 2
\n" ); document.write( " x= 1 y= 2 z= 3
\n" ); document.write( " \n" ); document.write( "

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