document.write( "Question 216615: QUESTION # 8
\n" ); document.write( "SOLVE BY THE ADITION METHOD:
\n" ); document.write( "x-5y-z=-5
\n" ); document.write( "2x-2y+z=-11
\n" ); document.write( "-x+2y-2z=11 \n" ); document.write( "

Algebra.Com's Answer #163677 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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SOLVE BY THE ADDITION METHOD:
\n" ); document.write( "x - 5y - z=-5
\n" ); document.write( "2x- 2y + z=-11
\n" ); document.write( "-x+ 2y -2z= 11
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by -1 and add
\n" ); document.write( "-x + 5y + z=+5
\n" ); document.write( "2x- 2y + z=-11
\n" ); document.write( "-x+ 2y -2z= 11
\n" ); document.write( "-------------------Addition eliminates x and z
\n" ); document.write( "0x + 5y +0z = 5
\n" ); document.write( "y = $\"5%2F5\"$
\n" ); document.write( "y = 1
\n" ); document.write( ";
\n" ); document.write( "use the 1st two equations, replace y with 1 and add
\n" ); document.write( "x - 5 - z=-5
\n" ); document.write( "2x- 2 + z=-11
\n" ); document.write( ":
\n" ); document.write( "x - z =-5 + 5
\n" ); document.write( "2x+ z=-11 + 2
\n" ); document.write( ":
\n" ); document.write( "x - z = 0
\n" ); document.write( "2x+ z =-9
\n" ); document.write( "---------------addition eliminates z
\n" ); document.write( "3x = -9
\n" ); document.write( "x = $\"%28-9%29%2F3\"$
\n" ); document.write( "x = -3
\n" ); document.write( ":
\n" ); document.write( "Use 2x + z = -9; replace x with -3
\n" ); document.write( "2(-3) + z = - 9
\n" ); document.write( "-6 + z = -9
\n" ); document.write( "z = -9 + 6
\n" ); document.write( "z = -3
\n" ); document.write( ":
\n" ); document.write( "x = -3; y = 1; z = -3
\n" ); document.write( ";
\n" ); document.write( ";
\n" ); document.write( "Check solutions in 3rd original equation
\n" ); document.write( "-x + 2y -2z = 11
\n" ); document.write( "-(-3) + 2(1) - 2(-3) = 11
\n" ); document.write( "+3 + 2 + 6 = 11 \n" ); document.write( "

\n" );