document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856324>Question 856324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x-3y-10=0 and x^2+xy+y^2+2x+y-6=0.                      Solve please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515919 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=515919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the linear equation for x in terms of y  (or the other way around if you want); substitute this into the conic section equation, and simplify.  You are looking to solve a quadratic equation in ONE variable which may have two solutions, or possibly one solution.  Can you do this without more help?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "\"No.\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y-10=0 ALIGN=MIDDLE  ALT=\"2x-3y-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=3y%2B10 ALIGN=MIDDLE  ALT=\"2x=3y%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x=%283%2F2%29y%2B5%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x=%283%2F2%29y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---Use this in the quadratic equation and again later after finding values for y.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "The substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y%2F2%2B5%29%5E2%2B%283y%2F2%2B5%29y%2By%5E2%2B2%283y%2F2%2B5%29%2By-6=0 ALIGN=MIDDLE  ALT=\"%283y%2F2%2B5%29%5E2%2B%283y%2F2%2B5%29y%2By%5E2%2B2%283y%2F2%2B5%29%2By-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F4%29y%5E2%2B15y%2B25%2B%283%2F2%29y%5E2%2B5y%2By%5E2%2B3y%2B10%2By-6=0 ALIGN=MIDDLE  ALT=\"%289%2F4%29y%5E2%2B15y%2B25%2B%283%2F2%29y%5E2%2B5y%2By%5E2%2B3y%2B10%2By-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...combine like terms and simplify ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829%2F4%29y%5E2%2B%2833%2F2%29y%2B29=0 ALIGN=MIDDLE  ALT=\"%2829%2F4%29y%5E2%2B%2833%2F2%29y%2B29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2829y%5E2%2B66y%2B116=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%2829y%5E2%2B66y%2B116=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ---- you could try to factor this, but much easier to use the general solution to a quadratic equation.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%5E2-4%2A29%2A116=4356-113456=-109100 ALIGN=MIDDLE  ALT=\"66%5E2-4%2A29%2A116=4356-113456=-109100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solution will contain an Imaginary component.  The discriminant is less than zero.<BR>\n" );
document.write( "!  you would expect the two graphs to share not any points; no intersections.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Another try done on paper but solving first for x instead of y in the linear equation and then substituting, gave me after simplifications, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2819x%5E2-46x%2B732=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%2819x%5E2-46x%2B732=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "and the discriminant, \"b^2-4*a*c\", is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28-53516%29 ALIGN=MIDDLE  ALT=\"highlight_green%28-53516%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a value less than zero.  This again means that the solution for x will contain an Imaginary component.  The given conic section and the given line DO NOT INTERSECT! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );