document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187062>Question 1187062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find points of intersection(x,y) of the following system of nonlinear equations.<BR>\n" );
document.write( "y=√x<BR>\n" );
document.write( "y=2x-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818005 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "We have two different expressions for y in terms of x; set them equal to each other and solve.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29=2x-6 ALIGN=MIDDLE  ALT=\"sqrt%28x%29=2x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4x%5E2-24x%2B36 ALIGN=MIDDLE  ALT=\"x=4x%5E2-24x%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-25x%2B36=0 ALIGN=MIDDLE  ALT=\"x%5E2-25x%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-9%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%284x-9%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9%2F4 ALIGN=MIDDLE  ALT=\"x=9%2F4\"   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;\" ><br><BR>\n" );
document.write( "We squared both sides of the equation at one point, so we need to check for extraneous solutions.<br><BR>\n" );
document.write( "(1) x = 9/4<BR>\n" );
document.write( "y = sqrt(x) = 3/2<BR>\n" );
document.write( "y = 2x-6 = 9/2-6 = -3/2<br><BR>\n" );
document.write( "The two expressions for y evaluate differently; x = 9/4 is not a solution to the original equation.<br><BR>\n" );
document.write( "(2) x = 4<BR>\n" );
document.write( "y = sqrt(4) = 2<BR>\n" );
document.write( "y = 2x-6 = 8-6 = 2<br><BR>\n" );
document.write( "x=4 is a solution; it is the only solution.<br><BR>\n" );
document.write( "ANSWER: (x,y) = (4,2) is the single intersection point.<br><BR>\n" );
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