document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54109>Question 54109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system graphically.<BR>\n" );
document.write( "2x+y=12<BR>\n" );
document.write( "2x+y=22\r<BR>\n" );
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document.write( "please show me how to graph this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36366 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=36366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Line 1) 2x+y=12<BR>\n" );
document.write( "Line 2) 2x+y=22<BR>\n" );
document.write( "This one has no solution, let me show you a quick way of seeing that.  Put both equations in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=mx%2Bb%29 ALIGN=MIDDLE  ALT=\"highlight%28y=mx%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > form; where m=slope and (0,b)= y-intercept.<BR>\n" );
document.write( "Line 1) 2x+y=12<BR>\n" );
document.write( "Line 1) -2x+2x+y=-2x+12<BR>\n" );
document.write( "Line 1) y=-2x+12<BR>\n" );
document.write( "Line 2) 2x+y=22<BR>\n" );
document.write( "Line 2) -2x+2x+y=-2x+22<BR>\n" );
document.write( "Line 2) y=-2x+22<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "So your 2 lines are:<BR>\n" );
document.write( "y=-2x+12<BR>\n" );
document.write( "y=-2x+22<BR>\n" );
document.write( "Notice that both the m's are the same, m=-2 and the b's are different, 12 and 22 they are parallel lines that will never touch.  <BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "Graphically:<BR>\n" );
document.write( "Let x=10 for the 1st equation:<BR>\n" );
document.write( "y=-2(10)+12<BR>\n" );
document.write( "y=-20+12<BR>\n" );
document.write( "y=-8<BR>\n" );
document.write( "Plot (10,-8)<BR>\n" );
document.write( "Let x=6 in the same equation:<BR>\n" );
document.write( "y=-2(6)+12<BR>\n" );
document.write( "y=-12+12<BR>\n" );
document.write( "y=0<BR>\n" );
document.write( "Plot (6,0)<BR>\n" );
document.write( "Connect the dots.<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Let x=10 in the second equation.<BR>\n" );
document.write( "y=-2(10)+22<BR>\n" );
document.write( "y=-20+22<BR>\n" );
document.write( "y=-2<BR>\n" );
document.write( "Plot (10,-2)<BR>\n" );
document.write( "Let x=6<BR>\n" );
document.write( "y=-2(6)+22<BR>\n" );
document.write( "y=-12+22<BR>\n" );
document.write( "y=10<BR>\n" );
document.write( "Plot (6,10)<BR>\n" );
document.write( "Connect the dots.<BR>\n" );
document.write( "This is what you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-2x%2B12%2C-2x%2B22%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C-2x%2B12%2C-2x%2B22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "See they don't intersect.  Therefore there's no solution!<BR>\n" );
document.write( "Happy Calculating!!!\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );