document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178178>Question 1178178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following system of equations.\r<BR>\n" );
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document.write( "5 x  - 4 y  = 1<BR>\n" );
document.write( "-10 x + 8 y  = -2\r<BR>\n" );
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document.write( "Please write your solution(s) in the ordered-pair form. <BR>\n" );
document.write( "If there is no solution, please type \"None\". <BR>\n" );
document.write( "If there are infinitely many solutions, then type \"Infinitely Many Solutions\". </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807371 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Consider the extended matrix. \r\n" );
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document.write( "It is easy to see that its rows are proportional.  \r\n" );
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document.write( "The proportionality coefficient is -2.\r\n" );
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document.write( "It means that one equation is equivalent to the other equation,\r\n" );
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document.write( "so FACTUALLY you have only one equation in two unknowns.\r\n" );
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document.write( "Such system has INFINITELY MANY solutions.\r\n" );
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document.write( "Take x as a FREE variable and express  y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-1%29%2F4 ALIGN=MIDDLE  ALT=\"%285x-1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  from the first equation.\r\n" );
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document.write( "You may give any value to x and calculate the respective value of y: each such a pair (x,y) will be a solution.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved and explained.\r<BR>\n" );
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document.write( "-------------\r<BR>\n" );
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document.write( "See the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of the linear system of two equations in two unknowns</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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