document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105280>Question 105280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the ordered pairs <BR>\n" );
document.write( "	(7, 1), (10, 0), (1, –3), (–8, 6)<BR>\n" );
document.write( "are solutions for the equation x + 3y = 10?<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 #76625 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=76625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   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 (7,1):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%29%2B3%2A%281%29=10 ALIGN=MIDDLE  ALT=\"%287%29%2B3%2A%281%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=10 ALIGN=MIDDLE  ALT=\"10=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (7,1) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   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 (10,0):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%29%2B3%2A%280%29=10 ALIGN=MIDDLE  ALT=\"%2810%29%2B3%2A%280%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=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=10=10 ALIGN=MIDDLE  ALT=\"10=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (10,0) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   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 (1,-3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2B3%2A%28-3%29=10 ALIGN=MIDDLE  ALT=\"%281%29%2B3%2A%28-3%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   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=-8=10 ALIGN=MIDDLE  ALT=\"-8=10\"   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 (1,-3) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   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 fourth solution (-8,6):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%2B3%2A%286%29=10 ALIGN=MIDDLE  ALT=\"%28-8%29%2B3%2A%286%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   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=10=10 ALIGN=MIDDLE  ALT=\"10=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (-8,6) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   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=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(7,1), (10,0), and (-8,6)\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=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the points (7,1), (10,0), (1,-3), and (-8,6)\r<BR>\n" );
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document.write( "Here we can see that the points (7,1), (10,0), and (-8,6) lie on the line (they are the green points). These are the solutions to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2Ay=10 ALIGN=MIDDLE  ALT=\"x%2B3%2Ay=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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