document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=632161>Question 632161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I cannot figure out how to solve systems by graphing. I have read and read but am so confused. I need to solve the system 2x+y=2; 6x+4y=12.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help me figure out the answer and show/explain how. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #398055 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=398055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have 2 straight lines. The best way to get an<BR>\n" );
document.write( "idea what they look like is to convert the equations<BR>\n" );
document.write( "from the standard form ( as they now are ) into<BR>\n" );
document.write( "the slope-intercept form<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+y+=+2+ ALIGN=MIDDLE  ALT=\"+2x+%2B+y+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+-2x+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6x+%2B+4+y+=+12+ ALIGN=MIDDLE  ALT=\"+6x+%2B+4+y+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+2y+=+6+ ALIGN=MIDDLE  ALT=\"+3x+%2B+2y+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+-3x+%2B+6+ ALIGN=MIDDLE  ALT=\"+2y+=+-3x+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(1) and (2) are now in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+m%2Ax+%2B+b+ ALIGN=MIDDLE  ALT=\"+y+=+m%2Ax+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+ ALIGN=MIDDLE  ALT=\"+m+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = slope and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = y - intercept<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "In (1), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-2+ ALIGN=MIDDLE  ALT=\"+m+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In (2), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-3+ ALIGN=MIDDLE  ALT=\"+m+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both slope are negative, which means they go from<BR>\n" );
document.write( "upper left to lower right on the graph, opposite to<BR>\n" );
document.write( "what a positive slope does<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you a point for free on each line. It<BR>\n" );
document.write( "is the y-intercept point which is (0,b), or<BR>\n" );
document.write( "(0, 2) for equation (1)<BR>\n" );
document.write( "(0,6) for equation (2)<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Now you just need 1 other point for both lines, and<BR>\n" );
document.write( "since 2 points determine a line, you can draw<BR>\n" );
document.write( "each line. Where the lines intersect is the solution<BR>\n" );
document.write( "to the system of lines<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "To find the other point, just plug in any value for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and read off the value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For example:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+-2x+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll pick <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;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2%2A1+%2B+2+ ALIGN=MIDDLE  ALT=\"+y+=+-2%2A1+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <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;\" ><BR>\n" );
document.write( "So, I have the point (1,0)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+-3x+%2B+6+ ALIGN=MIDDLE  ALT=\"+2y+=+-3x+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll pick <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+2+ ALIGN=MIDDLE  ALT=\"+x+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+-3%2A2+%2B+6+ ALIGN=MIDDLE  ALT=\"+2y+=+-3%2A2+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+0+ ALIGN=MIDDLE  ALT=\"+2y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <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;\" ><BR>\n" );
document.write( "So, I have the point (2,0)<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Now you have this information about the lines:<BR>\n" );
document.write( "Line (1):<BR>\n" );
document.write( "(0,2)<BR>\n" );
document.write( "(1,0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-2+ ALIGN=MIDDLE  ALT=\"+m+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Line (2):<BR>\n" );
document.write( "(0,6)<BR>\n" );
document.write( "(2,0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-3+ ALIGN=MIDDLE  ALT=\"+m+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "And that's all you need </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );