document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73874>Question 73874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by graphing.<BR>\n" );
document.write( "4x+2y=10<BR>\n" );
document.write( "    y=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52855 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=52855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x+2y=10<BR>\n" );
document.write( "    y=4<BR>\n" );
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document.write( "To solve this system by graphing, you draw the graphs of the two equations and look for<BR>\n" );
document.write( "the point where the two graphs cross.  At that crossing point the value of x and the value<BR>\n" );
document.write( "of y are the values that make both of these equations \"work.\"<BR>\n" );
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document.write( "Let's talk a little bit about the graphs of these two equations before we take a look at the<BR>\n" );
document.write( "the graphs.<BR>\n" );
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document.write( "We can use some math analysis on the first equation to quickly decide what its graph is.  <BR>\n" );
document.write( "like. Let's set x equal to zero in this equation.  If we do, what is the value of y? With<BR>\n" );
document.write( "x equal to zero we are left with 2y = 10 and after dividing both sides of this by 2 we<BR>\n" );
document.write( "have y = 5.  But where is the point (0,5)?  It's on the y-axis 5 units up from the origin! <BR>\n" );
document.write( "Easy to locate it.<BR>\n" );
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document.write( "Still on the first equation.  Let's now set the value of y equal to zero.  This reduces the<BR>\n" );
document.write( "equation to 4x = 10 and after dividing both sides by 4 we get x = 2.5.  Where is the point <BR>\n" );
document.write( "(2.5, 0) and it's on the x-axis 2.5 units to the right of the origin.  We now have two<BR>\n" );
document.write( "points on the graph of the first equation. We can plot them both and draw a line through them<BR>\n" );
document.write( "to obtain the graph.<BR>\n" );
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document.write( "Now what about the second graph, the graph of y = 4? This equation says to us that no<BR>\n" );
document.write( "matter what value we assign to x, the value of y is always +4.  So the points (-5,4), (0,4),<BR>\n" );
document.write( "10,4) are all points on this graph because they all have y values equal to 4. If you can<BR>\n" );
document.write( "picture this, you can see that the graph of y = 4 is a horizontal line through the point +4<BR>\n" );
document.write( "on the y-axis. <BR>\n" );
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document.write( "Wherever the graphs cross, the intersection point will have to have a value of y = 4 because<BR>\n" );
document.write( "of the second graph.  So look for the crossing point and get the corresponding value of<BR>\n" );
document.write( "x at  that point.<BR>\n" );
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document.write( "The graphs should look like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28500%2C500%2C-8%2C8%2C-8%2C8%2C-2x%2B5%2C4%29 ALIGN=MIDDLE  ALT=\"graph+%28500%2C500%2C-8%2C8%2C-8%2C8%2C-2x%2B5%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the use of graphing to solve linear equation sets.<BR>\n" );
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document.write( " </SPAN>\n" );
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