document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825817>Question 825817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the equation, 3x + 9y = -8, write a second linear equation to create a system that : <BR>\n" );
document.write( "Has exactly one solution. Explain your reasoning.<BR>\n" );
document.write( "Has no solution. Explain your reasoning. <BR>\n" );
document.write( "Has infinitely many solutions. Explain your reasoning. \r<BR>\n" );
document.write( "\n" );
document.write( "Part 2 : <BR>\n" );
document.write( " Interpret the meaning of the solution, if it exists, in the context of the graph of the following system of equations. <BR>\n" );
document.write( "{ -5x + 2y = 10<BR>\n" );
document.write( "{10x - 4y = -20   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497605 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=497605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the equation, 3x + 9y = -8, write a second linear equation to create a system that : <BR>\n" );
document.write( "Has exactly one solution. <BR>\n" );
document.write( "3x-9y=-8<BR>\n" );
document.write( "Explain your reasoning.<BR>\n" );
document.write( "The 1st has slope = -1/3<BR>\n" );
document.write( "The 2nd has slope = 1/3<BR>\n" );
document.write( "So the graphs intersect at one point:<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Has no solution.<BR>\n" );
document.write( "3x + 9y = 2<BR>\n" );
document.write( "Explain your reasoning.<BR>\n" );
document.write( "Both have the same slopes of -1/3 but different y-intercepts<BR>\n" );
document.write( "So the graphs do not intersect.<BR>\n" );
document.write( "================================== <BR>\n" );
document.write( "Has infinitely many solutions.<BR>\n" );
document.write( "6x + 18y = -16<BR>\n" );
document.write( " Explain your reasoning.<BR>\n" );
document.write( "One is a multiple of the other.<BR>\n" );
document.write( "The graphs are the same line; they intersect at every point.<BR>\n" );
document.write( "------------------------------- <BR>\n" );
document.write( "Part 2 : <BR>\n" );
document.write( "Interpret the meaning of the solution, if it exists, in the context of the graph of the following system of equations. <BR>\n" );
document.write( "{ -5x + 2y = 10<BR>\n" );
document.write( "{10x - 4y = -20<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Infinite number of solutions because<BR>\n" );
document.write( "the lower is -2 times the upper equation.<BR>\n" );
document.write( "They intersect at every point.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );