document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356552>Question 356552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system algebraically by the substitution method:\r<BR>\n" );
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document.write( "y= (x+1)^3<BR>\n" );
document.write( "y= sq rt of (x-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254853 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254853\">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=graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%28x%2B1%29%5E3%2Csqrt%28x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C10%2C-2%2C10%2C%28x%2B1%29%5E3%2Csqrt%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As you can see graphically, there is no solution (the curves never meet).<BR>\n" );
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document.write( "Since both expressions equal y set them equal to each other.<BR>\n" );
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document.write( "Use a substitution,<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%2B1 ALIGN=MIDDLE  ALT=\"u=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u-2=x-1 ALIGN=MIDDLE  ALT=\"u-2=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%5E3=sqrt%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%5E3=sqrt%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E3=sqrt%28u-2%29 ALIGN=MIDDLE  ALT=\"u%5E3=sqrt%28u-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E6=u-2 ALIGN=MIDDLE  ALT=\"u%5E6=u-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E6-u%2B2=0 ALIGN=MIDDLE  ALT=\"u%5E6-u%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E6-x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E6-x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As you can see there is no real solution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "All 6 solutions are complex.<BR>\n" );
document.write( "So then all 6 solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > will also be complex.<BR>\n" );
document.write( "There are no real solutions.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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