document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012365>Question 1012365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You solved a linear system and got the equation -6 = 0. How many solutions does the system of equations have? (Please Explain)\r<BR>\n" );
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document.write( "A. No solution<BR>\n" );
document.write( "B. Infinitely many solutions<BR>\n" );
document.write( "C. Exactly 1 solution<BR>\n" );
document.write( "D. 2 solutions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628262 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=628262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -6 = 0 means no solution.\r<BR>\n" );
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document.write( "that's because the statment is false.\r<BR>\n" );
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document.write( "if you got something like 1 = 1, then the statement will be true and you will get an infinite number of solutions.\r<BR>\n" );
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document.write( "two simple problems to illustrate.\r<BR>\n" );
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document.write( "first equation is 5x + 10y = 15<BR>\n" );
document.write( "second equation is 10x + 20y = 30\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "10x + 20y = 30<BR>\n" );
document.write( "10x + 20y = 30\r<BR>\n" );
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document.write( "when you subtract the second equation from the first, you will bget 0 + 0 = 0 which results in 0 = 0.\r<BR>\n" );
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document.write( "since this equation is true, you will get an infinite number of solutions and any value of x or y in the first equation will also solve the second equation as well.\r<BR>\n" );
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document.write( "if you graphed these two equations, you will see that they are identical.\r<BR>\n" );
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document.write( "if you converted them to slope intercept form and simpklified, you will see that they are the same equation.\r<BR>\n" );
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document.write( "now look at:\r<BR>\n" );
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document.write( "5x + 10y = 15<BR>\n" );
document.write( "10x + 20y = 45\r<BR>\n" );
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document.write( "multiply the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "10x + 20y = 30<BR>\n" );
document.write( "10x + 20y = 45\r<BR>\n" );
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document.write( "subtract first equation from second equation to get 0x + 0y = 15 which results in 0 = 15.\r<BR>\n" );
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document.write( "this equation is not true, therefore there is no solution.\r<BR>\n" );
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document.write( "if you graphed both these equations, you would see that they are parallel.\r<BR>\n" );
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document.write( "since they are parallel lines, they will never intersect therefore there is no solution common to both.\r<BR>\n" );
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document.write( "here's a graph of all 3 equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://theo.x10hosting.com/2016/010501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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