document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123498>Question 1123498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in the system below, I have only shown you the first equation. you fill in the second equation so that the systems will be...\r<BR>\n" );
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document.write( "A dependent: y=-3x+7\r<BR>\n" );
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document.write( "B:Inconsistent  y=-3x+7\r<BR>\n" );
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document.write( "C: A one solution system  y=-3x+7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739850 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=739850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> convert the equation into slope intercept form.\r<BR>\n" );
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document.write( "if the slope is the same and the y-intercept is the same, then the equations form an identical line and have an infinite number of solutions.\r<BR>\n" );
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document.write( "if the slope is the same and the y-intercept is different, then the equations form parallel lines and have no solutions.\r<BR>\n" );
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document.write( "otherwise, the equations will form lines that intersect at one common point on a two dimensional graphing plane.\r<BR>\n" );
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document.write( "since your equations are already in slope intercept form, then:\r<BR>\n" );
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document.write( "first equation is y = -3x + 7 and second equation is y = -3x + 7 leads to a common line which has an infinite number of solutions, i.e. all points on both lines are common to the other.\r<BR>\n" );
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document.write( "in standard form, they may not look like they're identical.<BR>\n" );
document.write( "in fact, they will probably be multiples of each other.\r<BR>\n" );
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document.write( "consider:\r<BR>\n" );
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document.write( "5x + 7y = 14<BR>\n" );
document.write( "10x + 14y = 28\r<BR>\n" );
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document.write( "divide the second equation by 2 to get 5x + 7y = 14.\r<BR>\n" );
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document.write( "first and second equation are the same, therefore will generate one common line where all points on the first line are common to all points on the second line.\r<BR>\n" );
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document.write( "first equation is y = -3x + 7 and second equation is y = -3x + 14\r<BR>\n" );
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document.write( "slope is the same but y-intercept is different.<BR>\n" );
document.write( "these equations are are parallel and will have no solution.\r<BR>\n" );
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document.write( "first equation is y = -3x + 7<BR>\n" );
document.write( "second equation is y = 5x + 7\r<BR>\n" );
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document.write( "these equations are neither parallel or identical, therefore they will have one common point between both of them.\r<BR>\n" );
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document.write( "the terminology is as follow:\r<BR>\n" );
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document.write( "the terminology from varsity tutors is as follows:\r<BR>\n" );
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document.write( "If a system has at least one solution, it is said to be consistent.\r<BR>\n" );
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document.write( "If a consistent system has exactly one solution, it is independent.\r<BR>\n" );
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document.write( "If a consistent system has an infinite number of solutions, it is dependent. <BR>\n" );
document.write( "When you graph the equations, both equations represent the same line.\r<BR>\n" );
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document.write( "If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.\r<BR>\n" );
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document.write( "under these definitions.\r<BR>\n" );
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document.write( "y = -3x + 7 and y = -3x + 7 is consistent and dependent because it has an infinite number of solutions.\r<BR>\n" );
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document.write( "y = -3x + 7 and y = -3x + 14 is inconsistent because it has no solutions.\r<BR>\n" );
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document.write( "y = -3x + 7 and y = 5x + 7 is consistent and independent because it has one solution.\r<BR>\n" );
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document.write( "the graphs of these equations are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091801.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091803.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.varsitytutors.com/hotmath/hotmath_help/topics/consistent-and-dependent-systems\" target = \"_blank\">https://www.varsitytutors.com/hotmath/hotmath_help/topics/consistent-and-dependent-systems</a>\r<BR>\n" );
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document.write( "here's another reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/systlin1.htm\" target = \"_blank\">https://www.purplemath.com/modules/systlin1.htm</a><BR>\n" );
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