document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=789093>Question 789093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me solve this?<BR>\n" );
document.write( "Solve the system by graphing both equations on the same axes. Give the ordered pair for the point of intersection.<BR>\n" );
document.write( "5x+5y=8 <BR>\n" );
document.write( "x=4-y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478745 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=478745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I can tell that the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285x%2B5y=8%2Cx=4-y%29 ALIGN=MIDDLE  ALT=\"system%285x%2B5y=8%2Cx=4-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no solution. The lines are parallel. There is no way to be completely sure that two lines are parallel just from the graph (You need to do some calculations), so either you have a typo or this the wrong problem, and can only confuse students.<BR>\n" );
document.write( " <BR>\n" );
document.write( "To graph one line you need to plot two points and connect them with a straight line.<BR>\n" );
document.write( "Using grid paper is recommended.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4-y ALIGN=MIDDLE  ALT=\"x=4-y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=4 ALIGN=MIDDLE  ALT=\"x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we have the point (0,4).<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we have the point (4,0).<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B5y=8 ALIGN=MIDDLE  ALT=\"5x%2B5y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > the same trick would give us points (0,8/5) and (8/5,0), which are too close together to draw the line accurately.<BR>\n" );
document.write( "We could substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=8 ALIGN=MIDDLE  ALT=\"5y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=8%2F5 ALIGN=MIDDLE  ALT=\"y=8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (0,8/5), and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4%2B5y=8 ALIGN=MIDDLE  ALT=\"5%2A4%2B5y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2B5y=8 ALIGN=MIDDLE  ALT=\"20%2B5y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y=-12 ALIGN=MIDDLE  ALT=\"5y=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-12%2F5=-10%262%2F5 ALIGN=MIDDLE  ALT=\"y=-12%2F5=-10%262%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for point (4,-12/5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2Cblue%28line%28-1%2C5%2C5%2C-1%29%29%2C%0D%0Ablue%28circle%280%2C4%2C0.15%29%29%2Cblue%28circle%284%2C0%2C0.15%29%29%2C%0D%0Agreen%28circle%280%2C8%2F5%2C0.15%29%29%2Cgreen%28circle%284%2C-12%2F5%2C0.15%29%29%2C%0D%0Agreen%28line%28-4%2C28%2F5%2C5%2C-17%2F5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > If you calculate the vertical distance between one green point and the blue one right above it, you realize that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F5 ALIGN=MIDDLE  ALT=\"12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-8%2F5=12%2F5 ALIGN=MIDDLE  ALT=\"4-8%2F5=12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-%28-12%2F5%29=12%2F5 ALIGN=MIDDLE  ALT=\"0-%28-12%2F5%29=12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That tells you that the lines are parallel.<BR>\n" );
document.write( "There is no intersection, and so there is no solution.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=4 ALIGN=MIDDLE  ALT=\"x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, multiplying both sides times 5 we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B5y=20 ALIGN=MIDDLE  ALT=\"5x%2B5y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B5y ALIGN=MIDDLE  ALT=\"5x%2B5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be equal to 20 and to 8 at the same time, it was obvious from the start that there was no solution.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );