document.write( "Question 24526: I am having trouble with this problem.\r
\n" ); document.write( "\n" ); document.write( "SOLVE THIS SYSTEM OF EQUATIONS, WHEN POSSIBLE...\r
\n" ); document.write( "\n" ); document.write( "x+y+z=4
\n" ); document.write( "x-y+2z=8
\n" ); document.write( "2x+y-z=3\r
\n" ); document.write( "\n" ); document.write( "I used the elimination method and broke this down into two equations with only two variables. I try to eliminate another variable, but cannot do it! HELP PLEASE!! \n" ); document.write( "

Algebra.Com's Answer #13050 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve:
\n" ); document.write( "1) $\"x%2By%2Bz+=+4\"$
\n" ); document.write( "2) $\"x-y%2B2z+=+8\"$
\n" ); document.write( "3) $\"2x%2By-z+=+3\"$ Add equations 1) and 2) to get:
\n" ); document.write( "4) $\"2x%2B3z+=+12\"$ Add equations 2) and 3) to get:
\n" ); document.write( "5) $\"3x%2Bz+=+11\"$ Multiply equation 5) by 3 to get:
\n" ); document.write( "6) $\"9x%2B3z+=+33\"$ Now subtract equation 4) from equation 6) to get:
\n" ); document.write( "7) $\"7x+=+21\"$ Divide both sides by 7.
\n" ); document.write( " $\"x+=+3\"$ Substitute this into equation 5) and solve for z.
\n" ); document.write( " $\"3%283%29%2Bz+=+11\"$
\n" ); document.write( " $\"9%2Bz+=+11\"$ Subtract 9 from both sides.
\n" ); document.write( " $\"z+=+2\"$ Finally, substitute x=3 and z=2 into equation 1) and solve for y.
\n" ); document.write( " $\"3%2By%2B2+=+4\"$
\n" ); document.write( " $\"y%2B5+=+4\"$ Subtract 5 from both sides.
\n" ); document.write( " $\"y+=+-1\"$ \r
\n" ); document.write( "\n" ); document.write( "Solution:
\n" ); document.write( "x = 3
\n" ); document.write( "y = -1
\n" ); document.write( "z = 2\r
\n" ); document.write( "\n" ); document.write( "Check by substituting these values into the three equations, 1), 2), and 3) \n" ); document.write( "

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