document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091985>Question 1091985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+1)^2-(y-1)^2=20, x^2-(y+2)^2= 24 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706521 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=706521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The solution already posted has an arithmetic error (or maybe just a typographical error) somewhere along the way.  Maybe you saw it....<br><BR>\n" );
document.write( "Step 1: If you expand everything in both equations, then you will have an x^2 and y^2 term in both equations; so when you compare the two equations by subtraction, the squared terms will cancel out, leaving you with a linear equation in x and y.<br><BR>\n" );
document.write( "Step 2: You can solve that linear equation for one of the variables and substitute into either of the original equations to solve for one variable; since you will be solving a quadratic equation, there will probably be two solutions.<br><BR>\n" );
document.write( "Step 3: substituting each of those values into one of the original equations will give you the corresponding values of the other variable.<br><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Step 1: Get a linear equation from the two given equations by expanding, then subtracting one equation from the other...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B2x%2B1%29-%28y%5E2-2y%2B1%29+=+20 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2B1%29-%28y%5E2-2y%2B1%29+=+20\"   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%2B2x-y%5E2%2B2y+=+20 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-y%5E2%2B2y+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y%5E2%2B4y%2B4%29+=+24 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y%5E2%2B4y%2B4%29+=+24\"   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-y%5E2-4y-4+=+24 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2-4y-4+=+24\"   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-y%5E2-4y+=+28 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2-4y+=+28\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6y+=+-8 ALIGN=MIDDLE  ALT=\"2x%2B6y+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (by subtracting (2) from (1))<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y+=+-4 ALIGN=MIDDLE  ALT=\"x%2B3y+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (3)<br><BR>\n" );
document.write( "Step 2: Solve (3) for x and substitute in the second original equation; solve the resulting quadratic equation for two values of y.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3y-4 ALIGN=MIDDLE  ALT=\"x+=+-3y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3y-4%29%5E2+-+%28y%2B2%29%5E2+=+24 ALIGN=MIDDLE  ALT=\"%28-3y-4%29%5E2+-+%28y%2B2%29%5E2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9y%5E2%2B24y%2B16-y%5E2-4y-4+=+24 ALIGN=MIDDLE  ALT=\"9y%5E2%2B24y%2B16-y%5E2-4y-4+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y%5E2%2B20y-12+=+0 ALIGN=MIDDLE  ALT=\"8y%5E2%2B20y-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2%2B5y-3+=+0 ALIGN=MIDDLE  ALT=\"2y%5E2%2B5y-3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y-1%29%28y%2B3%29+=+0 ALIGN=MIDDLE  ALT=\"%282y-1%29%28y%2B3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The two values for y are 1/2 and -3.<br><BR>\n" );
document.write( "Step 3: Find the corresponding x value for each y value, using (4).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%281%2F2%29-4+=+-11%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%281%2F2%29-4+=+-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%28-3%29-4+=+5 ALIGN=MIDDLE  ALT=\"x+=+-3%28-3%29-4+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The points of intersection of the two graphs (the pair of (x,y) values that satisfy both equations) are (-11/2,1/2) and (5,-3).<BR>\n" );
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