document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617760>Question 617760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve 3x + y = -8 <BR>\n" );
document.write( "               2x -y = -8   by graphing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388577 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=388577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect that you have a typo in your problem, because the solution does not involve whole numbers, as I would expect from that type of problem.<BR>\n" );
document.write( "Otherwise, maybe you are expected to use a graphing calculator.<BR>\n" );
document.write( "I cannot explain graphing calculators through this website.<BR>\n" );
document.write( "I will solve the problem as posted, graphing the old way, by hand.<BR>\n" );
document.write( "It will show you strategies to do that kind of solving, even if there was a typo.<BR>\n" );
document.write( "To graph each line you need 2 points.<BR>\n" );
document.write( "You chose the points aiming for easy calculations and a nice looking graph.<BR>\n" );
document.write( "For easiest calculations, I would set x=0 and x=-5 and solve for y.<BR>\n" );
document.write( "(Zeros are usually good choices, and I picked x=-5 because I saw it would give y values that would not be too large).<BR>\n" );
document.write( "For equation 3x + y = -8:<BR>\n" );
document.write( "x=0 --> y=-8 (That gives us point (0,-8)).<BR>\n" );
document.write( "x=-5 --> 3(-5)+y=-8 --> -15+y=-8 --> y=-8+15 --> y=7 for point (-5,7)<BR>\n" );
document.write( "For equation 2x - y = -8:<BR>\n" );
document.write( "x=0 --> -y=-8 --> y=8<BR>\n" );
document.write( "x=-5 --> 2(-5)-y=-8 --> -10-y=-8 --> -y=-8+10 --> -y=2 --> y=-2 for <BR>\n" );
document.write( "Now, for each equation, we plot the points and connect them with a straight line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-7%2C3%2C-10%2C10%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%280%2C-8%2C0.3%29%29%2Cred%28circle%28-5%2C7%2C0.3%29%29%2C%0D%0Ablue%28circle%280%2C8%2C0.3%29%29%2Cblue%28circle%28-5%2C-2%2C0.3%29%29%2C%0D%0Ared%28line%28-10%2C22%2C5%2C-23%29%29%2C%0D%0Ablue%28line%28-10%2C-12%2C5%2C18%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (The first equation is graphed in red, the second in blue, and the points are big circles).<BR>\n" );
document.write( "In a typical problem of this type, the lines would cross at a point with integer x and y coordinates. You would read those coordinates from the graph, substitute in the equations and verifty that it is a solution.<BR>\n" );
document.write( "Here they seen to cross at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%261%2F4=-3.25 ALIGN=MIDDLE  ALT=\"x=-3%261%2F4=-3.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > or maybe <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%261%2F5=-3.2 ALIGN=MIDDLE  ALT=\"x=-3%261%2F5=-3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is not a typical problem and that is going to make calculations more cumbersome.<BR>\n" );
document.write( "I checked x=-3.2 and got:<BR>\n" );
document.write( "for equation 3x + y = -8, 3(-3.2)+y=-8 --> -9.6+y=-8 --> y=1.6<BR>\n" );
document.write( "for equation 2x - y = -8, 2(-3.2)-y=-8 --> -6.4-y=-8 --> -y=-1.6 --> y=-1.6<BR>\n" );
document.write( "So the lines really cross at the point with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-3.2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-3.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=1.6%29 ALIGN=MIDDLE  ALT=\"highlight%28y=1.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and that is the solution.<BR>\n" );
document.write( "(I was betting on fifths because the slopes are 2 and 3, which adds to 5, and the equations could be the position of people walking towards each other at speeds of 2 miles and hour and 3 miles and hour, which would reduce the distance between them by 5 miles per hour). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );