document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74478>Question 74478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lines described by 3x-y=17, 2x+5y=17, x+2y=a+b, and x-y=3b-5a all pass through the same point. What is the ratio of a to b? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53467 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At that point, the x and y values are the same in all the equations.  Using the first two equations, you can find values for x and y; and then use those values in the third and fourth equations to find a and b.\r<BR>\n" );
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document.write( "From first equation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-17 ALIGN=MIDDLE  ALT=\"y=3x-17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting into second equation:     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B5%2A%283x-17%29=17 ALIGN=MIDDLE  ALT=\"2x%2B5%2A%283x-17%29=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "   so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and from first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using third equation:     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=a%2Bb ALIGN=MIDDLE  ALT=\"8=a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >  so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8-b ALIGN=MIDDLE  ALT=\"a=8-b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting into fourth equation:    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=3b-5%2A%288-b%29 ALIGN=MIDDLE  ALT=\"5=3b-5%2A%288-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "     so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=45%2F8 ALIGN=MIDDLE  ALT=\"b=45%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >   and from third equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=19%2F8 ALIGN=MIDDLE  ALT=\"a=19%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The ratio of a to b is 19:45 </SPAN>\n" );
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