document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194064>Question 1194064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following augmented matrix is in row echelon form and represents a linear system. Use​ back-substitution to solve the system if possible.<BR>\n" );
document.write( "[1 1 -1|2]<BR>\n" );
document.write( "[0 1 -1|2]<BR>\n" );
document.write( "[0 0  1|1]<BR>\n" );
document.write( "What is the solution to the linear​ system? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826159 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The bottom row indicates we have this equation<BR>\n" );
document.write( "0x+0y+1z = 1<BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "z = 1\r<BR>\n" );
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document.write( "The middle row says<BR>\n" );
document.write( "0x+1y+(-1)z = 2<BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "y-z = 2\r<BR>\n" );
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document.write( "Plug in z = 1 and solve for y<BR>\n" );
document.write( "y-z = 2<BR>\n" );
document.write( "y-1 = 2<BR>\n" );
document.write( "y = 2+1<BR>\n" );
document.write( "y = 3\r<BR>\n" );
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document.write( "The first line of the given augmented matrix says we have this equation<BR>\n" );
document.write( "1x+1y+(-1)z = 2<BR>\n" );
document.write( "aka<BR>\n" );
document.write( "x+y-z = 2\r<BR>\n" );
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document.write( "Plug in y = 3 and z = 1. Solve for x.<BR>\n" );
document.write( "x+y-z = 2<BR>\n" );
document.write( "x+3-1 = 2<BR>\n" );
document.write( "x+2 = 2<BR>\n" );
document.write( "x = 2-2<BR>\n" );
document.write( "x = 0\r<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "x = 0, y = 3, z = 1<BR>\n" );
document.write( "We can condense this into the ordered triple (x,y,z) = (0,3,1)<BR>\n" );
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