document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744166>Question 744166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need to solve this systems of equations using substitution\r<BR>\n" );
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document.write( "X^2+Y^2=25<BR>\n" );
document.write( "3X-4X=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453214 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X%5E2%2BY%5E2=25%2C3X-4X=0%29 ALIGN=MIDDLE  ALT=\"system%28X%5E2%2BY%5E2=25%2C3X-4X=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is easy.<BR>\n" );
document.write( "The only solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X-4X=0 ALIGN=MIDDLE  ALT=\"3X-4X=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=0 ALIGN=MIDDLE  ALT=\"X=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X-4X=0 ALIGN=MIDDLE  ALT=\"3X-4X=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-X=0 ALIGN=MIDDLE  ALT=\"-X=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28X=0%29 ALIGN=MIDDLE  ALT=\"highlight%28X=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=0 ALIGN=MIDDLE  ALT=\"X=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X%5E2%2BY%5E2=25 ALIGN=MIDDLE  ALT=\"X%5E2%2BY%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y%5E2=25 ALIGN=MIDDLE  ALT=\"Y%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "which has two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Y=5%29 ALIGN=MIDDLE  ALT=\"highlight%28Y=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Y=-5%29 ALIGN=MIDDLE  ALT=\"highlight%28Y=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions to the system are the two pairs (0,5) and (0,-5), or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28X=0%2CY=5%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28X=0%2CY=5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28X=0%2CY=-5%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28X=0%2CY=-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "If the problem had been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283X-4Y=0%2CX%5E2%2BY%5E2=25%29 ALIGN=MIDDLE  ALT=\"system%283X-4Y=0%2CX%5E2%2BY%5E2=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the system could be solved similarly, with a little more work.<BR>\n" );
document.write( "The answer is not pretty, so that was not the intended problem.<BR>\n" );
document.write( "(Classroom problems are supposed to have pretty answers).<BR>\n" );
document.write( "In that case, solving for X to substitute in the other equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X-4Y=0 ALIGN=MIDDLE  ALT=\"3X-4Y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X=4Y ALIGN=MIDDLE  ALT=\"3X=4Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=4Y%2F3 ALIGN=MIDDLE  ALT=\"X=4Y%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to substitute.<BR>\n" );
document.write( "So you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X=4Y%2F3%2CX%5E2%2BY%5E2=25%29 ALIGN=MIDDLE  ALT=\"system%28X=4Y%2F3%2CX%5E2%2BY%5E2=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284Y%2F3%29%5E2%2BY%5E2=25 ALIGN=MIDDLE  ALT=\"%284Y%2F3%29%5E2%2BY%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16Y%5E2%2F9%2BY%5E2=25 ALIGN=MIDDLE  ALT=\"16Y%5E2%2F9%2BY%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point, I would multiply both sides to the equal sign times 9 to get rid of fractions. I would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16Y%5E2%2B9Y%5E2=225 ALIGN=MIDDLE  ALT=\"16Y%5E2%2B9Y%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16Y%5E2%2B9Y%5E2-225=0 ALIGN=MIDDLE  ALT=\"16Y%5E2%2B9Y%5E2-225=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That equation yields two ugly solutions for Y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+%28-9+%2B-+sqrt%28+9%5E2-4%2A16%2A%28-225%29+%29%29%2F%282%2A16%29=%28-9+%2B-+sqrt%289%5E2%2B14400%29%29%2F32=%28-9+%2B-+sqrt%2814481%29%29%2F32=%28-9+%2B-+sqrt%289%2A1609%29%29%2F32=%28-9+%2B-+3sqrt%281609%29%29%2F32 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Each ugly Y can be substituted into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=4Y%2F3 ALIGN=MIDDLE  ALT=\"X=4Y%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the corresponding ugly X values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%284%2F3%29%28%28-9+%2B-+3sqrt%281609%29%29%2F32%29=%28-3+%2B-+sqrt%281609%29%29%2F8 ALIGN=MIDDLE  ALT=\"X=%284%2F3%29%28%28-9+%2B-+3sqrt%281609%29%29%2F32%29=%28-3+%2B-+sqrt%281609%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for a pair of ugly solutions. </SPAN>\n" );
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