document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70914>Question 70914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems by graphing.\r<BR>\n" );
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document.write( "x - 2y = 8<BR>\n" );
document.write( "3x - 2y = 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50657 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this system of equations by means of graphing you draw each graph and then <BR>\n" );
document.write( "identify the point where the two graphs cross.  The x and y values at that point are the<BR>\n" );
document.write( "values of x and y that will satisfy both equations.<BR>\n" );
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document.write( "The two equations to graph are:<BR>\n" );
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document.write( "x - 2y = 8<BR>\n" );
document.write( "3x - 2y = 12<BR>\n" );
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document.write( "You can graph the equations if you can find two points for each equation. An easy way to<BR>\n" );
document.write( "to this is pick one of the equations. Set x equal to zero (making the x term disappear)<BR>\n" );
document.write( "and then solve for y.  In the first (top) equation above, setting x equal to zero <BR>\n" );
document.write( "eliminates the x term and the equation becomes -2y = 8.  Solve by dividing both sides<BR>\n" );
document.write( "by -2 to get y = -4.  So we know that when x = 0 then y = -4.  This means that the point<BR>\n" );
document.write( "(0,-4) is on the graph.  Next we can do the same sort of thing only this time let<BR>\n" );
document.write( "y equal zero.  The term containing y disappears and the equation reduces to x = 8. So<BR>\n" );
document.write( "the point (8, 0) is also on the graph.  Plot these two points and draw a line through<BR>\n" );
document.write( "them and beyond in both directions. That completes the graph for the first equation.<BR>\n" );
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document.write( "Do the same sort of procedure for the second equation.  Set x equal to zero, making <BR>\n" );
document.write( "the term containing x disappear and leaving the equation -2y = 12.  Divide both sides<BR>\n" );
document.write( "of this equation by -2 to find that y = -6.  This makes a point that is on this graph<BR>\n" );
document.write( "(0, -6).  Return to the original equation and set y equal to zero. The term containing<BR>\n" );
document.write( "y disappears and you are left with 3x = 12.  Divide both sides by 3 to find that x = 4.<BR>\n" );
document.write( "So we know that (4, 0) is also on this second graph.  Plot the two points (0, -6) and <BR>\n" );
document.write( "(4, 0) and then draw a line through them and beyond.  <BR>\n" );
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document.write( "If you have graphed accurately you should now see the point where the two graphs cross.<BR>\n" );
document.write( "Find the x and y values for that point and they should satisfy both of the equations.<BR>\n" );
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document.write( "As a check you should find that the common or crossing point for the two graphs is (2, -3).<BR>\n" );
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document.write( "Hope this helps you to understand graphing of linear equations for the purpose of finding<BR>\n" );
document.write( "a common solution to the set of equations.<BR>\n" );
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