document.write( "Question 256815: Determine the value of (x + y + z) if, \r
\n" ); document.write( "\n" ); document.write( "3x – 2y – 3z = -1
\n" ); document.write( "6x + y + 2z = 7
\n" ); document.write( "9x + 3y + 4z = 9 \n" ); document.write( "

Algebra.Com's Answer #188847 by drk(1908) $\"\"$ $\"About$

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Here are the equations:
\n" ); document.write( "(i) 3x – 2y – 3z = -1
\n" ); document.write( "(ii) $\"6x+%2B+y+%2B+2z+=+7\"$
\n" ); document.write( "(iii) $\"9x+%2B+3y+%2B+4z+=+9\"$
\n" ); document.write( "step 1 - It may be easier to get rid of the y's first. We want to multiply by easy numbers. Multiply (ii) by 2 and add to (i) to get
\n" ); document.write( "(iv) 3x – 2y – 3z = -1
\n" ); document.write( "(v) $\"12x+%2B+2y+%2B+4z+=+14\"$
\n" ); document.write( "and then
\n" ); document.write( "(vi) $\"15x+%2B+1z+=+13\"$
\n" ); document.write( "step 2 - multiply (ii) by -3 and add to (iii) to get
\n" ); document.write( "(vii) $\"-18x+-+3y+-+6z+=+-21\"$
\n" ); document.write( "(viii) $\"9x+%2B+3y+%2B+4z+=+9\"$
\n" ); document.write( "and then
\n" ); document.write( "(ix) $\"-9x+-2z+=+-12\"$
\n" ); document.write( "Now, multiply (vi) by 2 and add to (ix) to get
\n" ); document.write( "(x) $\"30x+%2B+2z+=+26\"$
\n" ); document.write( "(xi) $\"-9x+-+2z+=+-12\"$
\n" ); document.write( "(xii) $\"21x+=+14\"$
\n" ); document.write( " $\"x+=+2%2F3\"$
\n" ); document.write( "Since x = 2/3, we sub that back into (x) to get
\n" ); document.write( " $\"z+=+3\"$
\n" ); document.write( "Now put those both back into (i) to get
\n" ); document.write( " $\"y+=+-3\"$
\n" ); document.write( "So we finally have {2/3, -3, 3} \n" ); document.write( "

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