document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245417>Question 245417</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Solving Systems by Graphing<BR>\n" );
document.write( "could some one show me how to do this<BR>\n" );
document.write( "3x-y=3 and 6x+y=5<BR>\n" );
document.write( "I have looked in my textbook,looked online i would like to know how to go about sovling these and how to get the plot points so i can graph them.<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179261 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=179261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solving Systems by Graphing<BR>\n" );
document.write( "could some one show me how to do this<BR>\n" );
document.write( "3x-y=3 <BR>\n" );
document.write( "Solve for y:<BR>\n" );
document.write( "y = 3x-3<BR>\n" );
document.write( "Plot two or more points:<BR>\n" );
document.write( "If x = 0, y = 3*0-3 = -3, giving you point (0,-3)<BR>\n" );
document.write( "If x = 2, y = 3*2-3 = 3, giving you point (2,3)<BR>\n" );
document.write( "Plot those two points and draw a line thru them<BR>\n" );
document.write( "to see the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x-3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "and 6x+y=5<BR>\n" );
document.write( "Solve for y:<BR>\n" );
document.write( "y = -6x+5<BR>\n" );
document.write( "Plot two or more points:<BR>\n" );
document.write( "If x = 0, y = -6*0+5 = 5, giving you point (0,5)<BR>\n" );
document.write( "If x = 1, y = -6*1+5 = -1, giving you point (1,-1)<BR>\n" );
document.write( "Plot those two points and draw a line thru them<BR>\n" );
document.write( "to see the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-6x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "To \"solve\" the system by graphing you have to put<BR>\n" );
document.write( "both of those lines on the same coordinate system<BR>\n" );
document.write( "and try to determine where the lines intersect.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x-3%2C-6x%2B5%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x-3%2C-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "Comment: Most problems of this type have a whole-number<BR>\n" );
document.write( "solution pair, like (2,3).  Your problem does not so<BR>\n" );
document.write( "it is virtually impossible to \"solve\" the system using<BR>\n" );
document.write( "the graphing technique.  Try to not let that fact <BR>\n" );
document.write( "frustrate your effors.<BR>\n" );
document.write( "The real solution to the system is best found using<BR>\n" );
document.write( "substitution or elimination.  Using substitution you<BR>\n" );
document.write( "would get:<BR>\n" );
document.write( "3x-3 = -6x+5<BR>\n" );
document.write( "9x = 8<BR>\n" );
document.write( "x = 8/9<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "y = 3x-3<BR>\n" );
document.write( "y = 3(8/9)-3 = 8/3 - 9/3 = -1/3<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "So the point of intersection of the two lines is <BR>\n" );
document.write( "(8/9 , - 1/3)<BR>\n" );
document.write( "====================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );