document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99123>Question 99123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This one really has me stumped. \r<BR>\n" );
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document.write( "Find the exact solution(s)of the system: x^2/4-y^2=1 and x=y^2+1\r<BR>\n" );
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document.write( "a. (4,&#8730;3),(4,-&#8730;3),(-4,&#8730;3),(-4,-&#8730;3)<BR>\n" );
document.write( "b. (4,&#8730;3),(-4,&#8730;3)<BR>\n" );
document.write( "c. (2,1),(2,-1),(4,&#8730;3),(4,-&#8730;3)<BR>\n" );
document.write( "d. (4,&#8730;3),(4,-&#8730;3)\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72135 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=72135\">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=x=y%5E2%2B1 ALIGN=MIDDLE  ALT=\"x=y%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=y%5E2 ALIGN=MIDDLE  ALT=\"x-1=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4-y%5E2=1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F4-y%5E2=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4-%28x-1%29=1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F4-%28x-1%29=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4=1%2B%28x-1%29+ ALIGN=MIDDLE  ALT=\"x%5E2%2F4=1%2B%28x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <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;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4=x+ ALIGN=MIDDLE  ALT=\"x%5E2%2F4=x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=4x+ ALIGN=MIDDLE  ALT=\"x%5E2=4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x=0+ ALIGN=MIDDLE  ALT=\"x%5E2-4x=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-4%29=0 ALIGN=MIDDLE  ALT=\"x%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=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=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" > Now solve for x in each case\r<BR>\n" );
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document.write( "Now let's use these two x-values to find the y-values\r<BR>\n" );
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document.write( "Let's find y when x=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2%2B1 ALIGN=MIDDLE  ALT=\"x=y%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=y%5E2%2B1 ALIGN=MIDDLE  ALT=\"0=y%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1=y%5E2 ALIGN=MIDDLE  ALT=\"-1=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29=y ALIGN=MIDDLE  ALT=\"sqrt%28-1%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides. Since you cannot take the square root of a negative number, x=0 is not in the solution\r<BR>\n" );
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document.write( "Let's find y when x=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2%2B1 ALIGN=MIDDLE  ALT=\"x=y%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=y%5E2%2B1 ALIGN=MIDDLE  ALT=\"4=y%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=y%5E2 ALIGN=MIDDLE  ALT=\"3=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B-sqrt%283%29=y ALIGN=MIDDLE  ALT=\"0%2B-sqrt%283%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides. So when x=4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0%2B-sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=0%2B-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"y=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So our solution is \r<BR>\n" );
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document.write( "(4,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (4,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "which means the answer is D </SPAN>\n" );
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