document.write( "Question 143785: Solve the following system of equations for the unknown variables.
\n" ); document.write( "3x + 3y = 3
\n" ); document.write( "-3x – 2z = -11
\n" ); document.write( "y + z = -1
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #104640 by nabla(475)\"\" \"About 
You can put this solution on YOUR website!
I'm going to solve this with matrices. You could solve this through substitution among other methods as well...
\n" ); document.write( "3 3 0 3
\n" ); document.write( "-3 0 -2 -11
\n" ); document.write( "0 1 1 -1\r
\n" ); document.write( "\n" ); document.write( "R1+R2--->\r
\n" ); document.write( "\n" ); document.write( "3 3 0 3
\n" ); document.write( "0 3 -2 -8
\n" ); document.write( "0 1 1 -1\r
\n" ); document.write( "\n" ); document.write( "1/3R1--->\r
\n" ); document.write( "\n" ); document.write( "1 1 0 1
\n" ); document.write( "0 3 -2 -8
\n" ); document.write( "0 1 1 -1\r
\n" ); document.write( "\n" ); document.write( "1/3R2-->
\n" ); document.write( "1 1 0 1
\n" ); document.write( "0 1 -2/3 -8/3
\n" ); document.write( "0 1 1 -1\r
\n" ); document.write( "\n" ); document.write( "-R2+R3-->
\n" ); document.write( "1 1 0 1
\n" ); document.write( "0 1 -2/3 -8/3
\n" ); document.write( "0 0 5/3 5/3\r
\n" ); document.write( "\n" ); document.write( "-R2+R1-->
\n" ); document.write( "1 0 2/3 11/3
\n" ); document.write( "0 1 -2/3 -8/3
\n" ); document.write( "0 0 5/3 5/3\r
\n" ); document.write( "\n" ); document.write( "3/5R3-->
\n" ); document.write( "1 0 2/3 11/3
\n" ); document.write( "0 1 -2/3 -8/3
\n" ); document.write( "0 0 1 1\r
\n" ); document.write( "\n" ); document.write( "2/3R3+R2-->
\n" ); document.write( "1 0 2/3 11/3
\n" ); document.write( "0 1 0 -2
\n" ); document.write( "0 0 1 1\r
\n" ); document.write( "\n" ); document.write( "-2/3R3+R1-->
\n" ); document.write( "1 0 0 3
\n" ); document.write( "0 1 0 -2
\n" ); document.write( "0 0 1 1\r
\n" ); document.write( "\n" ); document.write( "We can now read off the solution set:
\n" ); document.write( "{3,-2,1}.
\n" ); document.write( "check:
\n" ); document.write( "3(3) + 3(-2) = 9-6=3
\n" ); document.write( "-3(3) – 2(1) = -9-2=-11
\n" ); document.write( "-2 + 1 = -1
\n" ); document.write( " \n" ); document.write( "
\n" );