document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964814>Question 964814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -5y = +4x + 7<BR>\n" );
document.write( "-20x + py = -3\r<BR>\n" );
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document.write( "What value of p makes this system inconsistent? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589706 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve for y in both equations and place the solution in slope intercept form of y = mx + b here m is the slope and b is the y-intercept.\r<BR>\n" );
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document.write( "first equation is -5y = 4x + 7<BR>\n" );
document.write( "divide both sides of the equation by -5 to get:<BR>\n" );
document.write( "y = -4/5*x - 7/5<BR>\n" );
document.write( "m = -4/5<BR>\n" );
document.write( "b = -7/5\r<BR>\n" );
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document.write( "second equation is -20x + py = -3<BR>\n" );
document.write( "add 20x to both sides to get py = 20x - 3<BR>\n" );
document.write( "divide both sides by p to get y = 20x/p - 3/p<BR>\n" );
document.write( "m = 20x/p<BR>\n" );
document.write( "b = -3/p\r<BR>\n" );
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document.write( "for the system to be inconsistent, the lines have to be parallel.<BR>\n" );
document.write( "then there is no solution that is common to both lines.\r<BR>\n" );
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document.write( "the lines are parallel if their slopes are the same and their y-intercepts are different.\r<BR>\n" );
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document.write( "slope of the first line is -4/5<BR>\n" );
document.write( "slope of the second line is 20/p\r<BR>\n" );
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document.write( "you need to find the value of p that makes -4/5 equal to 20/p\r<BR>\n" );
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document.write( "set up the equation of -4/5 = 20/p\r<BR>\n" );
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document.write( "cross multiply to get -4p = 100<BR>\n" );
document.write( "divide by -4 to get p = 100/-4 which makes p = -25.\r<BR>\n" );
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document.write( "when p = -25, the equation of y = 20x/p -3 becomes y = 20x/-25 - 3/25.\r<BR>\n" );
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document.write( "simplify this to get y = -4/5 * x - 3/25.\r<BR>\n" );
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document.write( "the slope is the same and the y-intercept is different so the lines are parallel.\r<BR>\n" );
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document.write( "here's the graph of both equations.\r<BR>\n" );
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document.write( "first equation is y = -4/5 * x - 7/5<BR>\n" );
document.write( "second equation is y = -4/5 * x - 3/25\r<BR>\n" );
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document.write( "the lines are parallel.<BR>\n" );
document.write( "they will never intersect.<BR>\n" );
document.write( "the system is inconsistent which means that there is no solution.\r<BR>\n" );
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