document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=161503>Question 161503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 15. Three times one of the numbers is 11 less than 5 imes the other. The answer is 7 and 8. I just don't know how to set it up to solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118965 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 1 of the numbers<BR>\n" );
document.write( "y = the other number<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "sum of the numbers equals 15 in equation form becomes<BR>\n" );
document.write( "x + y = 15<BR>\n" );
document.write( "three times one of the numbers equals 11 less than 5 times the other number in equation form becomes<BR>\n" );
document.write( "3*x = 5*y - 11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "two equations to be solved simultaneously are:<BR>\n" );
document.write( "x + y = 15<BR>\n" );
document.write( "3*x = 5*y - 11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in the second equation, subtract 5*y from both sides to get<BR>\n" );
document.write( "3*x - 5*y = -11<BR>\n" );
document.write( "equations are now both in the same form of a*x + b*y = c reproduced below.<BR>\n" );
document.write( "x + y = 15<BR>\n" );
document.write( "3*x - 5*y = -11<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of the first eqution by 3 to get<BR>\n" );
document.write( "3*x + 3*y = 45<BR>\n" );
document.write( "3*x - 5*y = -11<BR>\n" );
document.write( "subtract the second equation from the first equation to get<BR>\n" );
document.write( "0*x + 8*y = 56<BR>\n" );
document.write( "effectively removing x from the equation to allow you to solve for y.<BR>\n" );
document.write( "this becomes<BR>\n" );
document.write( "8*y = 56<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "y = 7<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "original first equation is<BR>\n" );
document.write( "x + y = 15<BR>\n" );
document.write( "substituting 7 for y, we get<BR>\n" );
document.write( "x + 7 = 15<BR>\n" );
document.write( "subtracting 7 from both sides of the equation, we get<BR>\n" );
document.write( "x = 15 - 7<BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "x = 8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "second original equation is<BR>\n" );
document.write( "3*x = 5*y - 11<BR>\n" );
document.write( "substituting 7 for y and 8 for x, we get<BR>\n" );
document.write( "3*8 = 5*7 - 11<BR>\n" );
document.write( "24 = 35 - 11<BR>\n" );
document.write( "24 = 24<BR>\n" );
document.write( "proving the values for x and y are correct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answers are:<BR>\n" );
document.write( "x = 8<BR>\n" );
document.write( "y = 7\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );