document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112097>Question 112097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help!!!\r<BR>\n" );
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document.write( "Determine which of the ordered pairs are solutions for the given equation.\r<BR>\n" );
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document.write( "y=2x-1   (0,-2), (0,-1), (1/2,0), (3,-5)\r<BR>\n" );
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document.write( "Thanks so much<BR>\n" );
document.write( "Heather </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81798 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=81798\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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 (0,-2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29=2%2A%280%29-1 ALIGN=MIDDLE  ALT=\"%28-2%29=2%2A%280%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   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=-2=-1 ALIGN=MIDDLE  ALT=\"-2=-1\"   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 (0,-2) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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 (0,-1):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29=2%2A%280%29-1 ALIGN=MIDDLE  ALT=\"%28-1%29=2%2A%280%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > 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=-1=-1 ALIGN=MIDDLE  ALT=\"-1=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (0,-1) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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 (1/2,0):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29=2%2A%281%2F2%29-1 ALIGN=MIDDLE  ALT=\"%280%29=2%2A%281%2F2%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   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=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (1/2,0) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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 (3,-5):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29=2%2A%283%29-1 ALIGN=MIDDLE  ALT=\"%28-5%29=2%2A%283%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   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=-5=5 ALIGN=MIDDLE  ALT=\"-5=5\"   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 (3,-5) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(0,-1) and  (1/2,0) \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=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the points (0,-2), (0,-1), (1/2,0), and (3,-5)\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%2C10%2C%0D%0Agraph%28900%2C900%2C-10%2C10%2C-10%2C10%2C2%2Ax-1%29%2C%0D%0A%0D%0Acircle%280%2C-2%2C0.08%29%2C%0D%0Acircle%280%2C-2%2C0.10%29%2C%0D%0Acircle%280%2C-1%2C0.08%29%2C%0D%0Acircle%280%2C-1%2C0.10%29%2C%0D%0Acircle%281%2F2%2C0%2C0.08%29%2C%0D%0Acircle%281%2F2%2C0%2C0.10%29%2C%0D%0Acircle%283%2C-5%2C0.08%29%2C%0D%0Acircle%283%2C-5%2C0.10%29%2C%0D%0Agreen%28circle%280%2C-1%2C0.05%29%29%2C%0D%0Agreen%28circle%280%2C-1%2C0.08%29%29%2C%0D%0Agreen%28circle%281%2F2%2C0%2C0.05%29%29%2C%0D%0Agreen%28circle%281%2F2%2C0%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 (0,-1) and  (1/2,0)  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=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   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=y=2%2Ax-1 ALIGN=MIDDLE  ALT=\"y=2%2Ax-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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