document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735439>Question 735439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find out if 4x+14y=4 and 2x-14y=2 has a solution? and does it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449424 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=449424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Check if one equation is a factor of the other equation.  If yes then no solution.  If no then solution.  \r<BR>\n" );
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document.write( "Put your two equation into some desired form.  Standard form would be nice.<BR>\n" );
document.write( "They are both already in standard form.\r<BR>\n" );
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document.write( "Try factoring each equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282x%2B7y%29=2%282%29 ALIGN=MIDDLE  ALT=\"2%282x%2B7y%29=2%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-7y%29=2%281%29 ALIGN=MIDDLE  ALT=\"2%28x-7y%29=2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can probably see already, but next just simplify each equation through division of each member by 2, since each equation has factor of 2 for left and right members.<BR>\n" );
document.write( "Obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B7y=2 ALIGN=MIDDLE  ALT=\"2x%2B7y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7y=1 ALIGN=MIDDLE  ALT=\"x-7y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They are two DIFFERENT equations and are both linear in two variables.  They together CAN be a system and this system DOES YES have a solution, mainly because the slopes are not equal and so the two equations will intersect. </SPAN>\n" );
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