document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158969>Question 1158969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! <BR>\n" );
document.write( "I have been trying to use old, retired ACT exams to prepare to take the actual test, and in checking my work to find what I need to improve on I've run into a problem that I have solved but don't quite understand. \r<BR>\n" );
document.write( "\n" );
document.write( "\"The solution of the system of equations below is the set of all (x,y)such that 2x-3y=6. What is the value of k?\r<BR>\n" );
document.write( "\n" );
document.write( "18x-27y=54<BR>\n" );
document.write( "6x+ky=-2k\r<BR>\n" );
document.write( "\n" );
document.write( "A.-9<BR>\n" );
document.write( "B.-1<BR>\n" );
document.write( "C.3<BR>\n" );
document.write( "D.6<BR>\n" );
document.write( "E.9\r<BR>\n" );
document.write( "\n" );
document.write( "I solved by substituting each of the options given for k in the bottom equation, and then using the elimination method for solving systems of equations. However, it was very time consuming and I did not understand how the equation in the paragraph fit in with the other two equations. The answer was A. I did not understand why the answer that made the two equations come out to 0 was correct. I did not even use the equation in the paragraph to solve, and I only got the answer correct when fixing my work later, not when taking the test (I simulated an actual test as much as I could by timing myself). Is there a faster, more accurate method? Perhaps using the calculator? I do own a graphing calculator, but it is not a TI-84. \r<BR>\n" );
document.write( "\n" );
document.write( "I hope this makes sense. Thank you for taking the time to help me!\r<BR>\n" );
document.write( "\n" );
document.write( "Anna McLeran </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781965 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-27y=54 ALIGN=MIDDLE  ALT=\"18x-27y=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2Bky=-2k ALIGN=MIDDLE  ALT=\"6x%2Bky=-2k\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-27y=54 ALIGN=MIDDLE  ALT=\"18x-27y=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B3ky=-6k ALIGN=MIDDLE  ALT=\"18x%2B3ky=-6k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------subtract\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-27y-18x-3ky=54-%28-6k%29 ALIGN=MIDDLE  ALT=\"18x-27y-18x-3ky=54-%28-6k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-27y-3ky=54%2B6k ALIGN=MIDDLE  ALT=\"-27y-3ky=54%2B6k\"   DISABLED_style= \"max-width:90%; height:auto;\" >........group\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3ky-27y%29=%286k%2B54%29 ALIGN=MIDDLE  ALT=\"%28-3ky-27y%29=%286k%2B54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor out common\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y%28k+%2B+9%29+=+6%28k+%2B+9%29 ALIGN=MIDDLE  ALT=\"-3y%28k+%2B+9%29+=+6%28k+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y%28k+%2B+9%29-+6%28k+%2B+9%29=0 ALIGN=MIDDLE  ALT=\"-3y%28k+%2B+9%29-+6%28k+%2B+9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3y+-+6+%29%28k+%2B+9%29=0 ALIGN=MIDDLE  ALT=\"%28-3y+-+6+%29%28k+%2B+9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k+%2B+9%29=0 ALIGN=MIDDLE  ALT=\"%28k+%2B+9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-9%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3y-+6+=0 ALIGN=MIDDLE  ALT=\"-3y-+6+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=-6 ALIGN=MIDDLE  ALT=\"3y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-9%28-2%29=-2%28-9%29 ALIGN=MIDDLE  ALT=\"6x-9%28-2%29=-2%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B18=18 ALIGN=MIDDLE  ALT=\"6x%2B18=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=18-18 ALIGN=MIDDLE  ALT=\"6x=18-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=0 ALIGN=MIDDLE  ALT=\"6x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, check your system:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x-27y=54 ALIGN=MIDDLE  ALT=\"18x-27y=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2A0-27%28-2%29=54 ALIGN=MIDDLE  ALT=\"18%2A0-27%28-2%29=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54=54 ALIGN=MIDDLE  ALT=\"54=54\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> true\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2Bky=-2k ALIGN=MIDDLE  ALT=\"6x%2Bky=-2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A0-9%28-2%29=-2%28-9%29 ALIGN=MIDDLE  ALT=\"6%2A0-9%28-2%29=-2%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=18 ALIGN=MIDDLE  ALT=\"18=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >->true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );