document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161845>Question 1161845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the systems of equations algebraically, test each solution for validity, and then graph the system to check your number of solutions: \r<BR>\n" );
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document.write( "x^2-2y^2=2<BR>\n" );
document.write( "xy=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785536 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the systems of equations algebraically, test each solution for validity, and then graph the system to check your number of solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2y%5E2=2 ALIGN=MIDDLE  ALT=\"x%5E2-2y%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=2 ALIGN=MIDDLE  ALT=\"xy=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=2 ALIGN=MIDDLE  ALT=\"xy=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2........solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Fy+ ALIGN=MIDDLE  ALT=\"x=2%2Fy+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..eq.2a\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2y%5E2=2 ALIGN=MIDDLE  ALT=\"x%5E2-2y%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.1, substitute<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   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=%282%2Fy+%29%5E2-2y%5E2=2 ALIGN=MIDDLE  ALT=\"%282%2Fy+%29%5E2-2y%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >... solve for<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   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=4%2Fy%5E2-2y%5E2=2 ALIGN=MIDDLE  ALT=\"4%2Fy%5E2-2y%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....both sides multiply by <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-2y%5E4=2y%5E2 ALIGN=MIDDLE  ALT=\"4-2y%5E4=2y%5E2\"   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=2y%5E4%2B2y%5E2-4 ALIGN=MIDDLE  ALT=\"0=2y%5E4%2B2y%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"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=y%5E4%2By%5E2-2 ALIGN=MIDDLE  ALT=\"0=y%5E4%2By%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=y%5E4-y%5E2%2B2y%5E2-2 ALIGN=MIDDLE  ALT=\"0=y%5E4-y%5E2%2B2y%5E2-2\"   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=%28y%5E4-y%5E2%29%2B%282y%5E2-2%29=0 ALIGN=MIDDLE  ALT=\"%28y%5E4-y%5E2%29%2B%282y%5E2-2%29=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=y%5E2%28y%5E2-1%29%2B2%28y%5E2-1%29=0 ALIGN=MIDDLE  ALT=\"y%5E2%28y%5E2-1%29%2B2%28y%5E2-1%29=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=%28y%5E2%2B2%29%28y%5E2-1%29=0 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B2%29%28y%5E2-1%29=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=%28y+-+1%29+%28y+%2B+1%29+%28y%5E2+%2B+2%29=0 ALIGN=MIDDLE  ALT=\"%28y+-+1%29+%28y+%2B+1%29+%28y%5E2+%2B+2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+1%29+=0 ALIGN=MIDDLE  ALT=\"%28y+-+1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><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( "if   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+1%29+=0+ ALIGN=MIDDLE  ALT=\"%28y+%2B+1%29+=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><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( "if  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+%2B+2%29=0+ ALIGN=MIDDLE  ALT=\"%28y%5E2+%2B+2%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=-2 ALIGN=MIDDLE  ALT=\"y%5E2=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2%29 ALIGN=MIDDLE  ALT=\"sqrt%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Ai ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Fy ALIGN=MIDDLE  ALT=\"x=2%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2a , substitute <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=x=2%2F1 ALIGN=MIDDLE  ALT=\"x=2%2F1\"   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=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Fy+ ALIGN=MIDDLE  ALT=\"x=2%2Fy+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, substitute <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=x=2%2F-1 ALIGN=MIDDLE  ALT=\"x=2%2F-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=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "real solutions are:\r<BR>\n" );
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document.write( "<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;\" >, <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( "and\r<BR>\n" );
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document.write( "<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;\" >, <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( "test each solution for validity:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2y%5E2=2 ALIGN=MIDDLE  ALT=\"x%5E2-2y%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<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;\" >, <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2-2%2A1%5E2=2 ALIGN=MIDDLE  ALT=\"2%5E2-2%2A1%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-2=2 ALIGN=MIDDLE  ALT=\"4-2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2 ALIGN=MIDDLE  ALT=\"2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> solution valid\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=2 ALIGN=MIDDLE  ALT=\"xy=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >........<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;\" >, <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A%28-1%29=2 ALIGN=MIDDLE  ALT=\"-2%2A%28-1%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2 ALIGN=MIDDLE  ALT=\"2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> solution valid\r<BR>\n" );
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document.write( "graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%0D%0Acircle%282%2C1%2C.12%29%2Ccircle%28-2%2C-1%2C.12%29%2Clocate%282%2C1%2Cp%282%2C1%29%29%2Clocate%28-2%2C-1%2Cp%28-2%2C-1%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2%2Fx%2C-sqrt%28x%5E2+-+2%29%2Fsqrt%282%29%2Csqrt%28x%5E2+-+2%29%2Fsqrt%282%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );