document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116993>Question 116993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help.\r<BR>\n" );
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document.write( "Which of the ordered pairs is a solution for the equation 2x - 4y = 8\r<BR>\n" );
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document.write( "A)  (-4, -2),   B) (0, -2),  C) (-4, 0)  D) (0, 2)\r<BR>\n" );
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document.write( "Thanks<BR>\n" );
document.write( "JMS </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85069 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=85069\">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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   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 (-4,-2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28-4%29-4%2A%28-2%29=8 ALIGN=MIDDLE  ALT=\"2%2A%28-4%29-4%2A%28-2%29=8\"   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=-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=0=8 ALIGN=MIDDLE  ALT=\"0=8\"   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,-2) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   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,-2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%280%29-4%2A%28-2%29=8 ALIGN=MIDDLE  ALT=\"2%2A%280%29-4%2A%28-2%29=8\"   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=8=8 ALIGN=MIDDLE  ALT=\"8=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (0,-2) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   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 (-4,0):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28-4%29-4%2A%280%29=8 ALIGN=MIDDLE  ALT=\"2%2A%28-4%29-4%2A%280%29=8\"   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=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=-8=8 ALIGN=MIDDLE  ALT=\"-8=8\"   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 (-4,0) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   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 (0,2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%280%29-4%2A%282%29=8 ALIGN=MIDDLE  ALT=\"2%2A%280%29-4%2A%282%29=8\"   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=-8=8 ALIGN=MIDDLE  ALT=\"-8=8\"   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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==============================================================================\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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(0,-2)\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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the points (-4,-2), (0,-2), (-4,0), and (0,2)\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%2C1%2F2%2Ax-2%29%2C%0D%0A%0D%0Acircle%28-4%2C-2%2C0.08%29%2C%0D%0Acircle%28-4%2C-2%2C0.10%29%2C%0D%0Acircle%280%2C-2%2C0.08%29%2C%0D%0Acircle%280%2C-2%2C0.10%29%2C%0D%0Acircle%28-4%2C0%2C0.08%29%2C%0D%0Acircle%28-4%2C0%2C0.10%29%2C%0D%0Acircle%280%2C2%2C0.08%29%2C%0D%0Acircle%280%2C2%2C0.10%29%2C%0D%0Agreen%28circle%280%2C-2%2C0.05%29%29%2C%0D%0Agreen%28circle%280%2C-2%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 point (0,-2) 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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   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=2%2Ax-4%2Ay=8 ALIGN=MIDDLE  ALT=\"2%2Ax-4%2Ay=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means B) is the answer. </SPAN>\n" );
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