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 #781969 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "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<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">18x - 27y = 54 ----- eq (i)<BR>\n" );
document.write( "6x + ky = - 2k ----- eq (ii)<BR>\n" );
document.write( "18x + 3ky = - 6k --- Multiplying eq (ii) by 3 ----- eq (iii)<BR>\n" );
document.write( "18x - 27y =   54 --- eq (i)<BR>\n" );
document.write( "Looking at eqs (i) & (iii), and EQUATING terms, you'll see that 3ky = - 27y<BR>\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28matrix%281%2C5%2C+k%2C+%22=%22%2C+%28-+27y%29%2F%283y%29%2C+%22=%22%2C+-+9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You DON'T have to go any further, but just for the fun of it, when you EQUATE the right-side. you'll also see that - 6k = 54. <BR>\n" );
document.write( "Then, we get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28matrix%281%2C5%2C+k%2C+%22=%22%2C+54%2F%28-+6%29%2C+%22=%22%2C+-+9%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28matrix%281%2C5%2C+k%2C+%22=%22%2C+54%2F%28-+6%29%2C+%22=%22%2C+-+9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );