document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097059>Question 1097059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x - 2y= 2 +x <BR>\n" );
document.write( "8y -7x = -2y -2x<BR>\n" );
document.write( "using the system of equations above, what is the average of x and y? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711456 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's rewrite each equation so they will both be in the same order and in standard form:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4x - 2y = 2 + x =====> 3x - 2y = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "8y - 7x = -2y - 2x =====> -5x + 10y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " 3x -  2y = 2<BR>\n" );
document.write( "-5x + 10y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply the first equation by 5, giving us:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "15x - 10y = 10<BR>\n" );
document.write( "-5x + 10y = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can now add equation 1 to equation 2, giving us\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10x = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Dividing both sides of the equation by 10 will give us our x value:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now replace x with 1 in equation 1:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3(1) - 2y = 2 =====> 3 - 2y = 2 =====> -2y = -1 =====> y = 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now have our x and y values: x = 1 and y = 1/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We are asked to find the average of x and y.  To find the average of 2 numbers, add both numbers together and divide that result by 2.  So, in our case:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1 + 1/2 = 1.5 =====> 1.5 / 2 =====> 0.75 or 3/4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: 0.75 or 3/4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );