document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218986>Question 218986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations<BR>\n" );
document.write( "2x+y=1<BR>\n" );
document.write( "4x+2y=3<BR>\n" );
document.write( "My answer is that there is no solution.  Is that correct and if not what am I doing wrong? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164777 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=164777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are correct.<BR>\n" );
document.write( "There is no solution.<BR>\n" );
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document.write( "Reason was that you wound upo with 0 + 0 = 1 which is not true.<BR>\n" );
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document.write( "Your two equations are:<BR>\n" );
document.write( "2x + y = 1<BR>\n" );
document.write( "4x + 2y = 3<BR>\n" );
document.write( "Multiply both sides of the first equation to get:<BR>\n" );
document.write( "4x + 2y = 2<BR>\n" );
document.write( "4x + 2y = 3<BR>\n" );
document.write( "Subtract first equation from the second equation to get:<BR>\n" );
document.write( "0 + 0 = 1<BR>\n" );
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document.write( "Statement is not true, therefore no solutions.<BR>\n" );
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document.write( "Your equations turn out to be parallel lines.<BR>\n" );
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document.write( "Converting both of them from the standard form of ax + by = c to the slope-intercept form of y = mx + b, I get<BR>\n" );
document.write( "y = -2x + 1<BR>\n" );
document.write( "y = -2x + 3/2<BR>\n" );
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document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept<BR>\n" );
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document.write( "Your slopes are equal which indicates that the lines are parallel.<BR>\n" );
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document.write( "graph of both of these equations is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C1%2C-2%2C2%2C-2x%2B1%2C-2x%2B3%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C1%2C-2%2C2%2C-2x%2B1%2C-2x%2B3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );