document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825664>Question 825664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [ One number is greater by 6 than twice another number, but 3 times the smaller exceeds the greater by one. Find the numbers. ]\r<BR>\n" );
document.write( "\n" );
document.write( "Is this the right formula?<BR>\n" );
document.write( "Y= 2x + 6<BR>\n" );
document.write( "3x + y= 1<BR>\n" );
document.write( "I am not sure </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497479 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "it's important to define your variables right from the start.<BR>\n" );
document.write( "doing so allows you to follow the logic of the problem statement, in clear mathematical form:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = smaller number<BR>\n" );
document.write( "y = larger number<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 2x + 6<BR>\n" );
document.write( "3x = y + 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now you have a proper linear system:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2x - y = -6<BR>\n" );
document.write( "3x - y = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution:<BR>\n" );
document.write( "x = smaller number = 7<BR>\n" );
document.write( "y = larger number = 20<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "2 -1<BR>\n" );
document.write( "3 -1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "-1 1<BR>\n" );
document.write( "-3 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );