document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251998>Question 251998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve: 2x-2y=4 and 3y-x=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183732 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=183732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x - 2y = 4<BR>\n" );
document.write( "3y - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "presumably you want to solve them simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use the second equation to solve for y in terms of x and then use that value to substitute in the first equation to solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "second equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3y - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add x to both sides and subtract 1 from both sides to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3y - 1 = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the value of x in terms of y and substitute in the first equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x - 2y = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute 3y-1 for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2*(3y-1) - 2y = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify by performing indicated operatioons to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "6y - 2 - 2y = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4y - 2 = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add 2 to both sides of equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4y = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of equation by 4 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (6/4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute for y in the second equation and solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "second equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3y - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with (6/4) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3*(6/4) - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify by performing indicated operations to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(18/4) - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add x to both sides of this equation and subtract 1 from both sides of this equation to get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(18/4) - 1 = x\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( "x = (14/4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = (14/4)<BR>\n" );
document.write( "y = (6/4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute in both equations to confirm these values will solve both equations (both equations will be true)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2x - 2y = 4<BR>\n" );
document.write( "3y - x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these equations becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2*(14/4) - 2*(6/4) = 4<BR>\n" );
document.write( "3*(6/4) - (14/4) = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplifying, these equations become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "28/4 - 12/4 = 4<BR>\n" );
document.write( "18/4 - 14/4 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplifying further, these equations become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16/4 = 4<BR>\n" );
document.write( "4/4 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both these equations are true, so the values for x and y are good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = (14/4)<BR>\n" );
document.write( "y = (6/4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these answers are the same as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 3.5<BR>\n" );
document.write( "y = 1.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );