document.write( "Question 209868: how do I eliminate variables using the addition method?\r
\n" ); document.write( "\n" ); document.write( "2x-y+z=1
\n" ); document.write( "3x-3y+4z=5
\n" ); document.write( "4x-2y+3z=4 \n" ); document.write( "
Algebra.Com's Answer #158640 by ankor@dixie-net.com(22740)\"\" \"About 
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How do I eliminate variables using the addition method?
\n" ); document.write( "2x - y + z = 1
\n" ); document.write( "3x -3y +4z = 5
\n" ); document.write( "4x -2y +3z = 4
\n" ); document.write( ":
\n" ); document.write( "They have made it easy, multiply the 2nd equation by -1 (change the signs) & add
\n" ); document.write( "2x - y + z = 1
\n" ); document.write( "-3x+3y -4z = -5
\n" ); document.write( "4x -2y +3z = 4
\n" ); document.write( "------------------addition eliminates y and z
\n" ); document.write( "+3x = 0
\n" ); document.write( "x = 0
\n" ); document.write( ":
\n" ); document.write( "Using the original two equations without x;
\n" ); document.write( "-y + z = 1
\n" ); document.write( "-3y +4z = 5
\n" ); document.write( "Multiply the 1st equation by -4 and add
\n" ); document.write( "+4y -4z = -4
\n" ); document.write( "-3y +4z = 5
\n" ); document.write( "-----------------addition eliminates z
\n" ); document.write( "y = 1
\n" ); document.write( ":
\n" ); document.write( "Find z by substitution
\n" ); document.write( "-y + z = 1
\n" ); document.write( "-1 + z = 1
\n" ); document.write( "z = 1 + 1
\n" ); document.write( "z = 2
\n" ); document.write( ":
\n" ); document.write( "x=0, y=1, z=2
\n" ); document.write( ";
\n" ); document.write( "Check solution in original 3rd equation
\n" ); document.write( "4x -2y +3z = 4
\n" ); document.write( "4(0) - 2(1) + 3(2) = 4
\n" ); document.write( "0 - 2 + 6 = 4\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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