document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101287>Question 101287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the ordered pairs (6,3) and (4,13) and (4,3) are solutions for the equation;\r<BR>\n" );
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document.write( "5x+y=33 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #73772 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=73772\">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=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "Let's test the first solution (6,3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%286%29%2B%283%29=33 ALIGN=MIDDLE  ALT=\"5%286%29%2B%283%29=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=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=33=33 ALIGN=MIDDLE  ALT=\"33=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (6,3) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------Now lets test another solution-------\r<BR>\n" );
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document.write( "Let's test the second solution (4,13):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%284%29%2B%2813%29=33 ALIGN=MIDDLE  ALT=\"5%284%29%2B%2813%29=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13 ALIGN=MIDDLE  ALT=\"y=13\"   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=33=33 ALIGN=MIDDLE  ALT=\"33=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (4,13) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------Now lets test another solution-------\r<BR>\n" );
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document.write( "Let's test the third solution (4,3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%284%29%2B%283%29=33 ALIGN=MIDDLE  ALT=\"5%284%29%2B%283%29=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=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=23=33 ALIGN=MIDDLE  ALT=\"23=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (4,3) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the following ordered pairs are solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(6,3) and  (4,13) \r<BR>\n" );
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document.write( "Now let's graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2By=33 ALIGN=MIDDLE  ALT=\"5x%2By=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the points (6,3), (4,13), and (4,3)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28900%2C900%2C-10%2C10%2C-10%2C17%2C%0D%0Agraph%28900%2C900%2C-10%2C10%2C-10%2C17%2C-5%2Ax%2B33%29%2C%0D%0A%0D%0Acircle%286%2C3%2C0.08%29%2C%0D%0Acircle%286%2C3%2C0.10%29%2C%0D%0Acircle%284%2C13%2C0.08%29%2C%0D%0Acircle%284%2C13%2C0.10%29%2C%0D%0Acircle%284%2C3%2C0.08%29%2C%0D%0Acircle%284%2C3%2C0.10%29%2C%0D%0Agreen%28circle%286%2C3%2C0.05%29%29%2C%0D%0Agreen%28circle%286%2C3%2C0.08%29%29%2C%0D%0Agreen%28circle%284%2C13%2C0.05%29%29%2C%0D%0Agreen%28circle%284%2C13%2C0.08%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here we can see that the points (6,3) and  (4,13)  lie on the line (they are the green points).  Notice the other solutions are points that do not lie on the line. </SPAN>\n" );
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