document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21423>Question 21423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x+y=8<BR>\n" );
document.write( "y+3z=5<BR>\n" );
document.write( "z+2w=1<BR>\n" );
document.write( "5w+3x=9<BR>\n" );
document.write( "solve the equations for x,y,w,z </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10321 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x + y = 8<BR>\n" );
document.write( "y +  3z = 5\r<BR>\n" );
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document.write( "(a) solve each equation for y\r<BR>\n" );
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document.write( "y = 8 - 2x<BR>\n" );
document.write( "y = 5 - 3z\r<BR>\n" );
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document.write( "(b) solve the third equation for z\r<BR>\n" );
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document.write( "z + 2w = 1<BR>\n" );
document.write( "z = 1 - 2w\r<BR>\n" );
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document.write( "from (a)<BR>\n" );
document.write( "8 - 2x = 5 - 3z<BR>\n" );
document.write( "substitute (1-2w) for z, the result from (b)<BR>\n" );
document.write( "8 - 2x = 5 - 3(1-2w)<BR>\n" );
document.write( "8 - 2x = 5 - 3(1-2w)<BR>\n" );
document.write( "8 - 2x = 5 - 3 + 6w\r<BR>\n" );
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document.write( "(c) 8 - 2x = 2 + 6w\r<BR>\n" );
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document.write( "solve the fourth equation for x<BR>\n" );
document.write( "5w + 3x = 9<BR>\n" );
document.write( "3x = 9 - 5w<BR>\n" );
document.write( "x = 3 - (5/3)w<BR>\n" );
document.write( "substitute this result into (c)\r<BR>\n" );
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document.write( "8 -2(3 - (5/3)w) = 2 + 6w<BR>\n" );
document.write( "8 - 6 + (10/3)w = 2 + 6w<BR>\n" );
document.write( "8 - 6 - 2 = (8/3)w<BR>\n" );
document.write( "0 = (8/3)w<BR>\n" );
document.write( "w = 0<BR>\n" );
document.write( "from the fourth equation, <BR>\n" );
document.write( "5(0) +3x = 9<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "from the 1st equation,<BR>\n" );
document.write( "2(3) + y = 8<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "from the 2nd equation,<BR>\n" );
document.write( "(2) + 3z = 5<BR>\n" );
document.write( "z = 1\r<BR>\n" );
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document.write( "so,<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "z = 1<BR>\n" );
document.write( "w = 0<BR>\n" );
document.write( "plug these values back into all four equations to verify them\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );