document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352206>Question 352206</A>: <I><SPAN STYLE=\"word-break: break-all;\">         <BR>\n" );
document.write( "Suppose you need to solve a system of equations in which both equations represent lines.  How many solutions can your system have?  Select ALL that are possible. <BR>\n" );
document.write( "3, 0, infinitely many, 4, 1, 2\r<BR>\n" );
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document.write( "How many solutions does the following system of equations have? <BR>\n" );
document.write( "-x-3y=3<BR>\n" );
document.write( "x-6y= 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251682 by </B><A HREF=/tutors/aboutme.mpl?userid=sofiyac><B>sofiyac(983)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sofiyac><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=sofiyac><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=251682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> System of equations (lines) can have either no solution, 1 solution or infinitely many solutions.\r<BR>\n" );
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document.write( "-x-3y=3<BR>\n" );
document.write( "x-6y= 5<BR>\n" );
document.write( "Solve second equaiton for x by adding 6y to each side, so you get<BR>\n" );
document.write( "a) x=5+6y. Now plug that into the first equation for x so you get<BR>\n" );
document.write( "-(5+6y)-3y=3. Now distribute the minus and you get <BR>\n" );
document.write( "-5-6y-3y=3. Add like terms and you get<BR>\n" );
document.write( "-5-9y=3. Add 5 to each side of the equation and you get<BR>\n" );
document.write( "-9y=8. Divide each side by -9 and you get<BR>\n" );
document.write( "y=-8/9.  Now you plug that into the equation i market with letter a).<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2B6%28-8%2F9%29=5-16%2F3=%2815-16%29%2F3=-1%2F3 ALIGN=MIDDLE  ALT=\"x=5%2B6%28-8%2F9%29=5-16%2F3=%2815-16%29%2F3=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Thus you have only one solution to this problem, which is the point (-1/3,-8/9). The \"solution\" in lenear equations means thats where the two lines intersect/cross each other. </SPAN>\n" );
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