document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68532>Question 68532</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1579243258/algebrahomeworkh>Algebra 1 for Chirstian Schools</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 2x + y = 15 <BR>\n" );
document.write( "x + 2y = 18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48747 by </B><A HREF=/tutors/aboutme.mpl?userid=rmromero><B>rmromero(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rmromero><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=48747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are several Steps to Graph these equations.<BR>\n" );
document.write( "<br>One way is by Using the Slope - Intercept Form.<BR>\n" );
document.write( "1. Rewrite the equation to y = mx + b, where m = the slope and b = y-intercept.<BR>\n" );
document.write( "From --->2x + y = 15<BR>\n" );
document.write( "         y = -2x + 15 , m = -2 and b = 15 <BR>\n" );
document.write( "<br> To graph the b will help you plot the first point. Since b = 15, you point is located (0, 15).The m is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=change+in+y%2Fchange+in+x ALIGN=MIDDLE  ALT=\"change+in+y%2Fchange+in+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since m = -2, we can rewrite it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F1 ALIGN=MIDDLE  ALT=\"-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From point (0, 15), we will move 2 units down because 2 is negative and 1 unit right because 1 is positive. <BR>\n" );
document.write( "<br> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-2%29x%2B15%29 ALIGN=MIDDLE  ALT=\"graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-2%29x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "2. x + 2y = 18<BR>\n" );
document.write( "Rewrite the equation to y = mx + b.<BR>\n" );
document.write( "x + 2y = 18<BR>\n" );
document.write( "2y = -x + 18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2F2+%2B+9 ALIGN=MIDDLE  ALT=\"y+=+-x%2F2+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > , m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > b = 9 , <BR>\n" );
document.write( "From point (0, 9), we will move 1 unit down and 2 units right.\r<BR>\n" );
document.write( "\n" );
document.write( "<br> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-1%2F2%29x%2B9%29 ALIGN=MIDDLE  ALT=\"graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-1%2F2%29x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<br>If you want to combine the two equation, the graph looks like this.<BR>\n" );
document.write( "<br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-2%29x%2B15%2C+%28-1%2F2%29x%2B9%29 ALIGN=MIDDLE  ALT=\"graph+%28200%2C+200%2C+-2%2C+17%2C+-1%2C+17%2C+%28-2%29x%2B15%2C+%28-1%2F2%29x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br> Green line is the graph of x + 2y = 18 and the red line shows the graph of 2x + y = 15\r<BR>\n" );
document.write( "\n" );
document.write( "If you want to find the intersection of the graph: Here are the Steps using Substition method<BR>\n" );
document.write( "1. In either equation, solve for one variable in terms of the other.<BR>\n" );
document.write( "x + 2y = 18<BR>\n" );
document.write( "x = -2y +18<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "2. Substitute -2y + 18 for x in the other equation 2x + y = 15. Solve y.<BR>\n" );
document.write( "2x + y = 15 <BR>\n" );
document.write( "2(-2y+18) + y = 15<BR>\n" );
document.write( "-4y + 36 + y = 15<BR>\n" );
document.write( "-3y = -21<BR>\n" );
document.write( "y = 7<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "3. Substitute the result from step 2 in either equation. Solve for the other variable.<BR>\n" );
document.write( "2x + y = 15 , y = 7<BR>\n" );
document.write( "2x + 7 = 15<BR>\n" );
document.write( "2x = 8<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "4. Check the solution in both original equations.<BR>\n" );
document.write( "2x + y = 15 , x = 4 and y = 7<BR>\n" );
document.write( "2(4) + 7 = 15<BR>\n" );
document.write( "8 + 7 = 15<BR>\n" );
document.write( "15 = 15 ----------->> True\r<BR>\n" );
document.write( "\n" );
document.write( "<br><BR>\n" );
document.write( "x + 2y = 18, x = 4 and y = 7<BR>\n" );
document.write( "4 + 2(7) = 18<BR>\n" );
document.write( "4 + 14 = 18<BR>\n" );
document.write( "18 = 18 ---------->> True\r<BR>\n" );
document.write( "\n" );
document.write( "The Solution of the equation is x = 4 and y = 7, Meaning the graph will meet when x = 4 and y = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );