document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89697>Question 89697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would you solve this problem by substitution?<BR>\n" );
document.write( "x^2+y^2=9<BR>\n" );
document.write( "x+y=3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #65149 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=65149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=3 ALIGN=MIDDLE  ALT=\"x%2By=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-x ALIGN=MIDDLE  ALT=\"y=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%283-x%29%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283-x%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-x ALIGN=MIDDLE  ALT=\"y=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9-6x%2Bx%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2B9-6x%2Bx%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9-6x%2Bx%5E2-9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B9-6x%2Bx%5E2-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-6x=0 ALIGN=MIDDLE  ALT=\"2x%5E2-6x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x-3%29=0 ALIGN=MIDDLE  ALT=\"2x%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out 2x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=0 ALIGN=MIDDLE  ALT=\"2x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each factor equal to x\r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x\r<BR>\n" );
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document.write( "So we have x values <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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets find y with <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-0=3 ALIGN=MIDDLE  ALT=\"y=3-0=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So one solution is (0,3)\r<BR>\n" );
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document.write( "Lets find y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3-3=0 ALIGN=MIDDLE  ALT=\"y=3-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So another solution is (3,0)\r<BR>\n" );
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document.write( "Here's some visual proof\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+900%2C+900%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++grid%281%29%2C%0D%0A+++++++++circle%280%2C0%2C3%29%2C%0D%0A+++++++++graph%28+900%2C+900%2C+-10%2C+10%2C+-10%2C+10%2C3-x%29%2C%0D%0A+++++++++blue%28circle%283%2C0%2C0.05%29%29%2C%0D%0A+++++++++blue%28circle%283%2C0%2C0.08%29%29%2C%0D%0A+++++++++green%28circle%280%2C3%2C0.05%29%29%2C%0D%0A+++++++++green%28circle%280%2C3%2C0.08%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=9 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=3 ALIGN=MIDDLE  ALT=\"x%2By=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we can see that the intersections are (0,3) and (3,0). So this verifies our answer. </SPAN>\n" );
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