document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122363>Question 122363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I solve this system by graphing, and what would the coordinates be?<BR>\n" );
document.write( "2x + y = 4<BR>\n" );
document.write( "x + y = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89874 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=89874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x + y = 4<BR>\n" );
document.write( "x + y = 3<br>\r<BR>\n" );
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document.write( "well first off we need to solve those equations i.e. get those equations into y=mx+b form.<br>\r<BR>\n" );
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document.write( "y = -2x +4<BR>\n" );
document.write( "y = -x +3<br>\r<BR>\n" );
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document.write( "Now we can find one set of points by just looking at the y intercept(b values) of each equation.  The first equation has a y intercept at (0,4) and the second equation has a y intercept at (0,3).  To find the second set of points needed for graphing those two lines we can use 1 of 2 methods.<br>\r<BR>\n" );
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document.write( "Method 1- Set each equation equal to 0 and solve for x (finding the x-intercepts)<br>\r<BR>\n" );
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document.write( "-2x+4 = 0<BR>\n" );
document.write( "-2x = -4<BR>\n" );
document.write( "x = 2<br>\r<BR>\n" );
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document.write( "-x+3 = 0 <BR>\n" );
document.write( "-x = -3<BR>\n" );
document.write( "x = 3<br>\r<BR>\n" );
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document.write( "so the second point for the first equation would be (2,0).  The second point for the second equation would be (3,0).  So now we have the points (0,4) and (2,0) for the first equation and the points (0,3) and (3,0) for the second equation and now we can graph those lines and see where they intersect.<br>\r<BR>\n" );
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document.write( "Method 2- Using the slope<br>\r<BR>\n" );
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document.write( "All the slope(m) is is rise over run or the change in y value over the change in x value.  So all you need to do is add that change to your points and you will get your second points.  So for the first equation the slope is -2 which is the same as -2/1 so you need to move down to in the y direction and right one in the x direction.  So your new point becomes (0+1,4-2) or (1,2).  For the second equation the slope is -1 which is the same as -1/1 so you need to move down one in the y direction and right one in the x direction.  So your new point becomes (0+1,3-1) or (1,2).  So now your points are: for the first equation (0,4) and (1,2) and for the second equation (0,3) and (1,2) so now can graph your lines and see where they intersect. </SPAN>\n" );
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