document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097061>Question 1097061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2/3y + 1/4x = 2<BR>\n" );
document.write( "8y + 3x = a<BR>\n" );
document.write( "in this system of equations a is a constant.If the system has infinite solutions, what is the value of a? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711459 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order for a system to have infinitely many solutions, you must have a situation where, when you add the two equations in the system together, your result is 0 = 0. (zero on the left side of the equation and zero on the right) \r<BR>\n" );
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document.write( "To find the value of a so that the system has infinite solutions, let's start by getting rid of the fractions from equation 1 in our system.  To do this, we can multiply the entire equation by 12, which is the least common denominator.  This gives us\r<BR>\n" );
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document.write( "8y + 3x = 24\r<BR>\n" );
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document.write( "Notice how the left side of equation 1 now matches the left side of equation 2?\r<BR>\n" );
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document.write( "8y + 3x = 24<BR>\n" );
document.write( "8y + 3x = a\r<BR>\n" );
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document.write( "This tells us that in order for both equations to match, \"a\" MUST be 24.  So, if a is 24, let's try to solve our system.  What will happen?\r<BR>\n" );
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document.write( "First, we can multiply equation 1 by -1, giving us\r<BR>\n" );
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document.write( "-8y - 3x = -24<BR>\n" );
document.write( "8y + 3x = 24\r<BR>\n" );
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document.write( "Adding equation 1 and 2 together, we get:\r<BR>\n" );
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document.write( "0 = 0\r<BR>\n" );
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document.write( "Since 0 = 0, this system of linear equations has infinitely many solutions when a = 24.\r<BR>\n" );
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document.write( "Answer: a = 24 </SPAN>\n" );
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