document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023591>Question 1023591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve system by graphing, then find the point of intersection:<BR>\n" );
document.write( "y=x+5<BR>\n" );
document.write( "y=-x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639132 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=639132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each equation will be graphed as a straight line.<BR>\n" );
document.write( "Once they are graphed, the apparent intersection point will be located,<BR>\n" );
document.write( "and its coordinates are the apparent solution to the problem.<BR>\n" );
document.write( "Usually those values need to be verified, because sometimes appearances are deceiving.<BR>\n" );
document.write( "I will show how to graph each line separately first for clarity.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The line represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B5 ALIGN=MIDDLE  ALT=\"y=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > has<BR>\n" );
document.write( "a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the coefficient of x), ans<BR>\n" );
document.write( "a y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (meaning that (0,5) is the point where the line crosses the y-axis.<BR>\n" );
document.write( "Based on that information, we graph the line as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C7%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%280%2C5%2C0.1%29%29%2Cred%28circle%280%2C5%2C0.2%29%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C10%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , starting from (0,5), and moving from point to point to (1,6), (2,7),<BR>\n" );
document.write( "by increasing y by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as x increases by 1 (one square to thew left and one up),<BR>\n" );
document.write( "and also to (-1,4), (-2,3), (-3,2), (-4,1), and (-5,0),<BR>\n" );
document.write( "moving the opposite way, one square to the left and one down each time.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The line represented by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2B3 ALIGN=MIDDLE  ALT=\"y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has<BR>\n" );
document.write( "a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the coefficient of x), ans<BR>\n" );
document.write( "a y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (meaning that (0,3) is the point where the line crosses the y-axis.<BR>\n" );
document.write( "Based on that information, we graph the line as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C7%2C%0D%0Agrid%281%29%2C%0D%0Agreen%28circle%280%2C3%2C0.2%29%29%2C%0D%0Agreen%28line%28-5%2C8%2C5%2C-2%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , starting from (0,3), and moving from point to point to (1,2), (2,1), (3,0), (4,-1), and (5,-2),<BR>\n" );
document.write( "by increasing y by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as x increases by 1 (one square to the right and one down each time),<BR>\n" );
document.write( "and also to (-1,4), and (-2,5),<BR>\n" );
document.write( "moving the opposite way, one square to the left and one up each time.<BR>\n" );
document.write( " <BR>\n" );
document.write( "A graph with the two lines together looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-3%2C7%2C%0D%0Agrid%281%29%2C%0D%0Ared%28line%28-5%2C0%2C5%2C10%29%29%2C%0D%0Agreen%28line%28-5%2C8%2C5%2C-2%29%29%2C%0D%0Acircle%28-1%2C4%2C0.2%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The lines appear to intersect at (-1,4), with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=-1%2Cy=4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=-1%2Cy=4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and we know that (-1,4) was a point we went through as we drew each line,<BR>\n" );
document.write( "so verification seems pointless in this case.<BR>\n" );
document.write( "However, verification may still be expected,<BR>\n" );
document.write( "and it would be needed if we had drawn the lines some other way.<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=-1%2B5=4 ALIGN=MIDDLE  ALT=\"x%2B5=-1%2B5=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B3=-%28-1%29%2B3=1%2B3=4 ALIGN=MIDDLE  ALT=\"-x%2B3=-%28-1%29%2B3=1%2B3=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which verifies solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28x=-1%2Cy=4%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28x=-1%2Cy=4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );