document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419240>Question 419240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations\r<BR>\n" );
document.write( "\n" );
document.write( "x+3y=4 (1)<BR>\n" );
document.write( "x=5-3y (2)\r<BR>\n" );
document.write( "\n" );
document.write( "the solution is??  or there is no solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293220 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the way the equations are set up, you can solve by substitution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute for x from the second equation into the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 3y = 4 becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 - 3y + 3y = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since this is not true, your equations do not have a common solution and the graph of the lines do not cross.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to graph these equations, solve for y in each equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 3y = 4 becomes y = (4-x)/3 = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 5 - 3y becomes y = (5-x)/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if we place these lines into the standard slope intercept form, we will see that they have the same slope and a different y intercept and therefore they are parallel to each other meaning they will never intersect.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (4-x)/3 becomes y = 4/3 - x/3 which becomes y = -(1/3)*x + 4/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (5-x)/3 becomes y = 5/3 - x/3 which becomes y = -(1/3)*x + 5/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the slope intercept form of the equations is y = mx + b where m is the slope and b is the y intercept.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can see that the slope of both these equations is the same and the y intercept is different.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means the lines are parallel to each other and will never intersect.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph of these equations is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%285-x%29%2F3%2C%284-x%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%285-x%29%2F3%2C%284-x%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );