document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477813>Question 477813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A TWO DIGIT NUMBER IS 7 TIMES THE SUM OF THE DIGITS. THE DIGITS GET INTERCHANGED IF 27 IS SUBTRACTED FROM THE NUMBER. FIND THE NUMBER </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327430 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=327430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your 2 digits are x and y<BR>\n" );
document.write( "10x + y = 7(x+y) is your first equation<BR>\n" );
document.write( "10x + y - 27 = 10y + x is your second equation.<BR>\n" );
document.write( "you need to solve these 2 equations simultaneously to get your answer.<BR>\n" );
document.write( "before doing that, simplify each equation to get:<BR>\n" );
document.write( "10x + y = 7(x+y) becomes:<BR>\n" );
document.write( "10x + y = 7x + 7y<BR>\n" );
document.write( "subtract 7x from both sides of the equation and subtract 7y from both sides of the equation to get:<BR>\n" );
document.write( "3x - 6y = 0<BR>\n" );
document.write( "hold on to that for now.<BR>\n" );
document.write( "10x + y - 27 = 10y + x is your second equation.<BR>\n" );
document.write( "add 27 to both sides of that equation and subtract 10y from both sides of the equation and subtract x from both sides of the equation to get:<BR>\n" );
document.write( "9x - 9y = 27<BR>\n" );
document.write( "hold on to that for now.<BR>\n" );
document.write( "your 2 equations after being simplified are:<BR>\n" );
document.write( "3x - 6y = 0<BR>\n" );
document.write( "9x - 9y = 27<BR>\n" );
document.write( "multiply both sides of the first equation by 3 to get:<BR>\n" );
document.write( "9x - 18y = 0<BR>\n" );
document.write( "9x - 9y = 27<BR>\n" );
document.write( "subtract the first equation from the second equation to get:<BR>\n" );
document.write( "9y = 27<BR>\n" );
document.write( "divide both sides of this equation by 9 to get:<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "substitute for y in the first equation of 3x - 6y = 0 to get:<BR>\n" );
document.write( "3x - 18 = 0<BR>\n" );
document.write( "add 18 to both sides of this equation to get:<BR>\n" );
document.write( "3x = 18<BR>\n" );
document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "your answers appear to be:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "your first original equation says:<BR>\n" );
document.write( "10x + y = 7(x+y)<BR>\n" );
document.write( "substitute for x and y to get:<BR>\n" );
document.write( "63 = 7(9)<BR>\n" );
document.write( "this becomes 63 = 63 which is true, so the value for x and y plugged into the first original equation are good.<BR>\n" );
document.write( "your second original equation says:<BR>\n" );
document.write( "10x + y - 27 = 10y + x<BR>\n" );
document.write( "substitute for x and y to get:<BR>\n" );
document.write( "63 - 27 = 36<BR>\n" );
document.write( "this becomes 36 = 36 which is true, so the value for x and y plugged ihto the second original equation are good.<BR>\n" );
document.write( "your digits are 6 and 3.<BR>\n" );
document.write( "the number is 63.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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