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" );
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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" );
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document.write( "18x-27y=54<BR>\n" );
document.write( "6x+ky=-2k\r<BR>\n" );
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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" );
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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" );
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document.write( "I hope this makes sense. Thank you for taking the time to help me!\r<BR>\n" );
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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 #781960 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=781960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -------------------------------<BR>\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?<BR>\n" );
document.write( "18x-27y=54<BR>\n" );
document.write( "6x+ky=-2k <BR>\n" );
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document.write( "The first equation of the system<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=2%2A3%2A3x-3%2A3%2A3y=2%2A3%2A3%2A3 ALIGN=MIDDLE  ALT=\"2%2A3%2A3x-3%2A3%2A3y=2%2A3%2A3%2A3\"   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=6 ALIGN=MIDDLE  ALT=\"2x-3y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------the same equation refered in the descriptive part before your listing of the equations of the system.\r<BR>\n" );
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document.write( "Your equation using k shows a coefficent on x being 6.  The way to get the simplified equation to have this same coefficient is multiply 2x-3y=6 by 3.  This gives you:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-9y=18 ALIGN=MIDDLE  ALT=\"6x-9y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Compare the corresponding parts.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%286=6%2C+-9=k%2C+18=-2k%29 ALIGN=MIDDLE  ALT=\"system%286=6%2C+-9=k%2C+18=-2k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-9 ALIGN=MIDDLE  ALT=\"k=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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