document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206622>Question 206622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Im a little confused with this problem. I tried to figure it out, but do not know what would be the right answer.\r<BR>\n" );
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document.write( "Solve by the elimination method.<BR>\n" );
document.write( "5x+6y=5<BR>\n" );
document.write( "10x+12y=10 <BR>\n" );
document.write( "what is the solution of the system?\r<BR>\n" );
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document.write( "( I came up with - The solution is (10,10).\r<BR>\n" );
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document.write( "but could the answer be that there are infinetely many solutions, or that there is no solution. can you please help. thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156160 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=156160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x+6y=5<BR>\n" );
document.write( "10x+12y=10<BR>\n" );
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document.write( "multiply first equation by 2 to get:<BR>\n" );
document.write( "10x + 12y = 10<BR>\n" );
document.write( "10x + 12y = 10<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract second equation from first to get:<BR>\n" );
document.write( "0 + 0 = 0<BR>\n" );
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document.write( "I believe the answer is that this is an identity and that any value of x and y that satisfied one equation would also satisfy the other.<BR>\n" );
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document.write( "if you graph both these equations, you would probably see that they are the same line.<BR>\n" );
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document.write( "first equation:<BR>\n" );
document.write( "5x + 6y = 5<BR>\n" );
document.write( "solving for y we get:<BR>\n" );
document.write( "6y -5x + 5<BR>\n" );
document.write( "y = -(5/6)x + (5/6)<BR>\n" );
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document.write( "second equation:<BR>\n" );
document.write( "10x + 12y = 10<BR>\n" );
document.write( "solving for y we get:<BR>\n" );
document.write( "12y = -10x + 10<BR>\n" );
document.write( "y = (-10/12)x + (10/12)<BR>\n" );
document.write( "which can be reduced to:<BR>\n" );
document.write( "y = (-5/6)x + (5/6)<BR>\n" );
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document.write( "the equations are identical after simplification.<BR>\n" );
document.write( " </SPAN>\n" );
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