document.write( "Question 253952: x+y-2z=0
\n" ); document.write( "3x+y=1
\n" ); document.write( "5x+3y+7z=2\r
\n" ); document.write( "\n" ); document.write( "x=
\n" ); document.write( "y=
\n" ); document.write( "z= \n" ); document.write( "

Algebra.Com's Answer #186338 by drk(1908) $\"\"$ $\"About$

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We have three equations:
\n" ); document.write( "(i) $\"x%2By-2z=0\"$
\n" ); document.write( "(ii) $\"3x%2By=1\"$
\n" ); document.write( "(iii) $\"5x%2B3y%2B7z=2\"$
\n" ); document.write( "solve (ii) for y. We get
\n" ); document.write( "(iv) $\"y+=+-3x+%2B+1\"$
\n" ); document.write( "substitute (iv) into (i) and (iii) to get 2 equations with two variables.
\n" ); document.write( "(v) $\"x%2B%28-3x%2B1%29-2z=0\"$
\n" ); document.write( "(vi) $\"5x%2B3%28-3x%2B1%29%2B7z=2\"$
\n" ); document.write( "simplify (v) and (vi) to get
\n" ); document.write( "(vii) $\"-2x-2z=-1%7D%7D%0D%0A%28viii%29+%7B%7B%7B-4x%2B7z=-1\"$
\n" ); document.write( "multiply (vii) by -2 to get
\n" ); document.write( "(ix) $\"4x+%2B+4z+=+2\"$
\n" ); document.write( "(viii) $\"-4x+%2B+7z+=+-1\"$
\n" ); document.write( "add down to eliminate x and solve for z. We get
\n" ); document.write( "(x) 11z = 1 - -> z = 1/11.
\n" ); document.write( "Find x.
\n" ); document.write( "x = 9/11
\n" ); document.write( "Find y.
\n" ); document.write( "y = -16/22
\n" ); document.write( "So, we have
\n" ); document.write( "{9/22 , -5/22 , 1/11} \n" ); document.write( "

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