document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207947>Question 207947</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321578295/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Twice one number minus a second number is five.  Twice the second number plus the first number is eight.  Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157382 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let your first number = x<BR>\n" );
document.write( "let your second number = y<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Twice the first number minus a second number is five.<BR>\n" );
document.write( "equation for this is:<BR>\n" );
document.write( "2x - y = 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Twice the second number plus the first number is eight.<BR>\n" );
document.write( "equation for this is:<BR>\n" );
document.write( "2y + x = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "from the first equation you can solve for y to get y = 2x-5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can substitute for y in the second equation to get:<BR>\n" );
document.write( "2 * (2x - 5) + x = 8<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "4x - 10 + x = 8<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "5x - 10 = 8<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "5x = 18<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "x = 3.6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can substitute for x in the first equation to get:<BR>\n" );
document.write( "2 * 3.6 - y = 5<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "7.2 - y = 5<BR>\n" );
document.write( "add y to both sides of this equation and subtract 5 from both sides of this equation to get:<BR>\n" );
document.write( "y = 7.2 - 5<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "y = 2.2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you have x = 3.6<BR>\n" );
document.write( "and y = 2.2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute in first equation to get:<BR>\n" );
document.write( "2 * 3.6 - 2.2 = 5 which becomes 7.2 - 2.2 = 5 which becomes 5 = 5<BR>\n" );
document.write( "substitute in second equation to get:<BR>\n" );
document.write( "2 * 2.2 + 3.6 = 8 which becomes 4.5 + 3.6 = 8 which becomes 8 = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answers prove out correct and are:<BR>\n" );
document.write( "x = 3.6<BR>\n" );
document.write( "y = 2.2<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );