document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122610>Question 122610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of these ordered pairs is a solution for the equation 3x-2y=6?<BR>\n" );
document.write( "(a)(0,-3)<BR>\n" );
document.write( "(b)(0,3)<BR>\n" );
document.write( "(c)(-2,0)<BR>\n" );
document.write( "(d)(-2,-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90031 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=90031\">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=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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 possible solution (0,-3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%280%29-2%2A%28-3%29=6 ALIGN=MIDDLE  ALT=\"3%2A%280%29-2%2A%28-3%29=6\"   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=-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=6=6 ALIGN=MIDDLE  ALT=\"6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Since the two sides of the equation are equal, this means (0,-3) is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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 possible solution (0,3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%280%29-2%2A%283%29=6 ALIGN=MIDDLE  ALT=\"3%2A%280%29-2%2A%283%29=6\"   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=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=-6=6 ALIGN=MIDDLE  ALT=\"-6=6\"   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 (0,3) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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  possible solution (-2,0):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-2%29-2%2A%280%29=6 ALIGN=MIDDLE  ALT=\"3%2A%28-2%29-2%2A%280%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   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=-6=6 ALIGN=MIDDLE  ALT=\"-6=6\"   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 (-2,0) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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  possible solution (-2,-3):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-2%29-2%2A%28-3%29=6 ALIGN=MIDDLE  ALT=\"3%2A%28-2%29-2%2A%28-3%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   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=0=6 ALIGN=MIDDLE  ALT=\"0=6\"   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 (-2,-3) is <font size=4><b>not</b></font> a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(0,-3)\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=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plot the points (0,-3), (0,3), (-2,0), and (-2,-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%2C10%2C%0D%0Agraph%28900%2C900%2C-10%2C10%2C-10%2C10%2C3%2F2%2Ax-3%29%2C%0D%0A%0D%0Acircle%280%2C-3%2C0.08%29%2C%0D%0Acircle%280%2C-3%2C0.10%29%2C%0D%0Acircle%280%2C3%2C0.08%29%2C%0D%0Acircle%280%2C3%2C0.10%29%2C%0D%0Acircle%28-2%2C0%2C0.08%29%2C%0D%0Acircle%28-2%2C0%2C0.10%29%2C%0D%0Acircle%28-2%2C-3%2C0.08%29%2C%0D%0Acircle%28-2%2C-3%2C0.10%29%2C%0D%0Agreen%28circle%280%2C-3%2C0.05%29%29%2C%0D%0Agreen%28circle%280%2C-3%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,-3) lie on the line (it is the green point). These are the solutions to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   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=3%2Ax-2%2Ay=6 ALIGN=MIDDLE  ALT=\"3%2Ax-2%2Ay=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the answer is A) </SPAN>\n" );
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