document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170972>Question 1170972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following pair of equations graphically\r<BR>\n" );
document.write( "\n" );
document.write( "2x - 3y = 1<BR>\n" );
document.write( "1.25x + 0.5y = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795839 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=795839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph is shown below.<BR>\n" );
document.write( "the intersection point is (x,y = (2,1).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/120301.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these are two equations that need to be solved simultaneously.<BR>\n" );
document.write( "one way to do that is shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x - 3y = 1<BR>\n" );
document.write( "1.25x + .5y = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the second equation by 6 and leave the first equation as is to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x - 3y = 1<BR>\n" );
document.write( "7.5x + 3y = 18\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add the two equations together to get:<BR>\n" );
document.write( "9.5x = 19<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 19/9.5 = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the first equation, replace x with 2 to get:<BR>\n" );
document.write( "2x - 3y = 1 becomes 4 - 3y = 1.<BR>\n" );
document.write( "add 3y to both sides of the equation and subtract 1 from both sides of the equation to get:<BR>\n" );
document.write( "4 - 1 = 3y<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "3 = 3y<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 3/3 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that (x,y) = (2,1).<BR>\n" );
document.write( "same solution as on the graph.\r<BR>\n" );
document.write( "<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" );