document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163463>Question 163463</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh>elementary and intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP I JUST DON'T UNDERSTAND THESE PROBLEMS AND I DON'T KNOW WHAT TO DO. PLEASE HELP ME....\r<BR>\n" );
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document.write( ": Graphical Representation of Linear Equations\r<BR>\n" );
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document.write( "1.	Plot the graph of the equations 3x - 8y = 5 and 4x - 2y = 11 and interpret the result. \r<BR>\n" );
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document.write( "2.	Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result. \r<BR>\n" );
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document.write( "3.	Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120431 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> : Graphical Representation of Linear Equations<BR>\n" );
document.write( "1. Plot the graph of the equations 3x - 8y = 5 and 4x - 2y = 11 and interpret the result.<BR>\n" );
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document.write( "First. you want to get equations into the general form, to plot the graphs<BR>\n" );
document.write( "3x - 8y = 5<BR>\n" );
document.write( "-8y = -3x + 5<BR>\n" );
document.write( "y has to be positive, multiply equation by -1<BR>\n" );
document.write( "8y = 3x - 5<BR>\n" );
document.write( "Divide equation by 8 to get 1y or just y:<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "4x - 2y = 11<BR>\n" );
document.write( "-2y = -4x + 11<BR>\n" );
document.write( "2y = 4x - 11; multiplied by -1 again<BR>\n" );
document.write( "y = 2x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F2 ALIGN=MIDDLE  ALT=\"11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; divided by 2<BR>\n" );
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document.write( "Using these two equation, plot two points for each by substituting a value for x<BR>\n" );
document.write( "and finding the value for y (I assume you know how to do that, if not email me)<BR>\n" );
document.write( "1st equation: y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8 ALIGN=MIDDLE  ALT=\"3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >; Green<BR>\n" );
document.write( " x | y<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "-1 |-1<BR>\n" );
document.write( "+3 |+.5; <BR>\n" );
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document.write( "2nd equation: y = 2x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F2 ALIGN=MIDDLE  ALT=\"11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >; purple<BR>\n" );
document.write( " x | y<BR>\n" );
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document.write( "-2 |-6.2<BR>\n" );
document.write( "+3 |+3.8<BR>\n" );
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document.write( "Plot these two graph and it should look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+6%2C+-6%2C+6%2C+2x-5.5%2C+%283%2F8%29x-%285%2F8%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-6%2C+6%2C+2x-5.5%2C+%283%2F8%29x-%285%2F8%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the graph we can see that they intersect at x/y coordinates: 3,.5<BR>\n" );
document.write( "That is interpreted as the solution to this system of two equations<BR>\n" );
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document.write( "You can prove this, substitute 3, for x and .5 for y i the 1st original equation<BR>\n" );
document.write( "3x - 8y = 5 <BR>\n" );
document.write( "3(3) - 8(.5) = 4<BR>\n" );
document.write( "9 - 4 = 5<BR>\n" );
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document.write( "Do the same in the 2nd original equation:<BR>\n" );
document.write( "4x - 2y = 11<BR>\n" );
document.write( "4(3) - 2(.5) = <BR>\n" );
document.write( "12 - 1 = 11<BR>\n" );
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document.write( "We know that these coordinates are the solution to these two equation<BR>\n" );
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document.write( "I am running out of time right now.  See how you do, let me know. I will have time later today to work on this.  Carl\r<BR>\n" );
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document.write( "2. Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result.<BR>\n" );
document.write( "3. Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result. </SPAN>\n" );
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