document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62650>Question 62650</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072918861/algebrahomeworkh>Algebra for college students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> hello\r<BR>\n" );
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document.write( "solve by graphing to show independent, inconsistent or dependent:\r<BR>\n" );
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document.write( "2x - 3y = 12<BR>\n" );
document.write( "3y - 2x = -12\r<BR>\n" );
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document.write( "tks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #43437 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=43437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve by graphing to show independent, inconsistent or dependent:\r<BR>\n" );
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document.write( "E1:  2x - 3y = 12<BR>\n" );
document.write( "E2:  3y - 2x = -12<BR>\n" );
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document.write( "Lines that are different and intersect at one point are independent.  (the books I'm working out of also call them consistent because they have a solution.)<BR>\n" );
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document.write( "Parallel lines are inconstistent because they will never intersect and have no solution.  (the books I'm working out of say that they are also independent because they are not the same line.)<BR>\n" );
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document.write( "Lines that lie right on top of each other are dependent, because graphically they are the same line.  (the cooks I'm working out of also call them consistent because they have a solution.  There are infinitely many solutions though, because the lines have all points in common.<BR>\n" );
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document.write( "E1:  2x - 3y = 12<BR>\n" );
document.write( "E2:  3y - 2x = -12<BR>\n" );
document.write( ": For E1, let x=0 and solve for y:<BR>\n" );
document.write( "2(0)-3y=12<BR>\n" );
document.write( "0-3y=12<BR>\n" );
document.write( "-3y/-3=12/-3<BR>\n" );
document.write( "y=-4  Plot (0,-4)<BR>\n" );
document.write( "Now let y=0 and solve for x:<BR>\n" );
document.write( "2x-3(0)=12<BR>\n" );
document.write( "2x-0=12<BR>\n" );
document.write( "2x/2=12/2<BR>\n" );
document.write( "x=6  Plot (6,0)<BR>\n" );
document.write( "Connect the points and you have this line: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-2x%2B12%29%2F-3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-2x%2B12%29%2F-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ": For E2, let x=0 and solve for y:<BR>\n" );
document.write( "3y-2(0)=-12<BR>\n" );
document.write( "3y=-12<BR>\n" );
document.write( "3y/3=-12/3<BR>\n" );
document.write( "y=-4  Plot (0,-4)<BR>\n" );
document.write( "Now let y=0 and solve for x:<BR>\n" );
document.write( "3(0)-2x=-12<BR>\n" );
document.write( "0-2x=-12<BR>\n" );
document.write( "-2x/-2=-12/-2<BR>\n" );
document.write( "x=6  Plot (6,0)<BR>\n" );
document.write( "Notice that these lines have the same x and y intercepts.  Any lines that share two points in common, share all points in common:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-2x%2B12%29%2F-3%2C%282x-12%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C%28-2x%2B12%29%2F-3%2C%282x-12%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both lines are graphed above, it looks like one line, therefore the system is dependent.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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