document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887699>Question 887699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following systems graphically\r<BR>\n" );
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document.write( "-x+3y=8\r<BR>\n" );
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document.write( "x+y=2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536822 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=536822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To graph a line all you need is two points on that line.  You can either pick points and plug them into the equations given or, and this is how I will do it, you can get both equations into slope intercept form which will give you the two points you need to graph each line.<br>\r<BR>\n" );
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document.write( "So first we need to solve each equation for y to get it into slope intercept form.<br>\r<BR>\n" );
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document.write( "-x+3y = 8 add x to both sides<BR>\n" );
document.write( "3y = 8+x divide both sides by 3<BR>\n" );
document.write( "y = 8/3 + 1/3x<br>\r<BR>\n" );
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document.write( "x+y=2 subtract x from both sides<BR>\n" );
document.write( "y = 2-x<br>\r<BR>\n" );
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document.write( "Now that we have both equations in slope intercept form we can look at each equation individually.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8%2F3%2B%281%2F3%29x ALIGN=MIDDLE  ALT=\"y=8%2F3%2B%281%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells us that the y intercept is 8/3 and the slope is 1/3.  So we know that the graph goes through the point (0,8/3) from the y-intercept.  And remembering that slope is the change in y over the change in x we know that the graph then goes up one and over 3.  So our new point would be (0+3,8/3+1) or (3,11/3).  You can plot these two points and then connect the points with the line.<br>\r<BR>\n" );
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document.write( "Next we look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2-x ALIGN=MIDDLE  ALT=\"y+=+2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The y intercept is 2 and the slope is -1.  So we know that the graph goes through the point (0,2) from the y-intercept.  Moving down 1 and over 1 puts our next point at (0+1,2-1) or (1,1).  Plotting these two points will yield your line.<br>\r<BR>\n" );
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document.write( "To finish this problem you will look to see where the two lines intersect.  This will be your solution.  I will leave this for you to do.  \r<BR>\n" );
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