document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147891>Question 147891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When solving equations by graphing, I get confused if fractions are involved. <BR>\n" );
document.write( "For example:\r<BR>\n" );
document.write( "\n" );
document.write( "9x – 5y = 20     and                                        \r<BR>\n" );
document.write( "\n" );
document.write( "First equation                                                  <BR>\n" );
document.write( " Let x = 0                                                          <BR>\n" );
document.write( "-5y = 20                                                            <BR>\n" );
document.write( "divide both sides by -5                                     <BR>\n" );
document.write( "y = -4                                                                 <BR>\n" );
document.write( "    <BR>\n" );
document.write( "Let y = 0                                                            <BR>\n" );
document.write( "9x = 20                                                              <BR>\n" );
document.write( "Divide both sides by 9                                       <BR>\n" );
document.write( "X = 20/9 or 2 and 2/9                                        <BR>\n" );
document.write( "     <BR>\n" );
document.write( "I would plot on a graph the two points                    <BR>\n" );
document.write( "(0, -4)<BR>\n" );
document.write( "(2 2/9, 0)  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Second equation\r<BR>\n" );
document.write( "\n" );
document.write( "5y – 9x = -20  <BR>\n" );
document.write( "Let x = 0<BR>\n" );
document.write( "5y= -20<BR>\n" );
document.write( "divide both sides by 5<BR>\n" );
document.write( "y = -4<BR>\n" );
document.write( "let y = 0<BR>\n" );
document.write( "-9x = -20<BR>\n" );
document.write( "Divide both sides by -9<BR>\n" );
document.write( "x = -20/-9 or 20/9 or 2 2/9<BR>\n" );
document.write( "I would plot on the graph the two pints<BR>\n" );
document.write( "  (0, -4)       (2 2/9, 0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Both equations are the same. Am I doing this correctly?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108265 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, you are doing it correctly.<BR>\n" );
document.write( "Let's look at the equations to see why. <BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-5y=20 ALIGN=MIDDLE  ALT=\"9x-5y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y-9x=-20 ALIGN=MIDDLE  ALT=\"5y-9x=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Re-arrange eq.2, x first then y,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9x%2B5y=-20 ALIGN=MIDDLE  ALT=\"-9x%2B5y=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, multiply both sides of eq. 2 by (-1),<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x-5y=20 ALIGN=MIDDLE  ALT=\"9x-5y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You end up with eq. 1.<BR>\n" );
document.write( "So yes, eq. 1 and eq. 2 are the same equation, as you already found out.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "With regards to fractions, remember they're just numbers. <BR>\n" );
document.write( "Maybe it's easier to change them to their approximate decimal values especially when graphing. <BR>\n" );
document.write( "Instead of (2 2/9,0) maybe try (2.2,0). <BR>\n" );
document.write( "It's usually close enough for graphing. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );