document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419240>Question 419240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following system of equations\r<BR>\n" );
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document.write( "x+3y=4 (1)<BR>\n" );
document.write( "x=5-3y (2)\r<BR>\n" );
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document.write( "the solution is??  or there is no solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293226 by </B><A HREF=/tutors/aboutme.mpl?userid=duckness73><B>duckness73(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=duckness73><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=duckness73><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets look carefully at these equations:\r<BR>\n" );
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document.write( "x + 3y = 4<BR>\n" );
document.write( "x = 5 - 3y\r<BR>\n" );
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document.write( "If we substitute the expression of x from the second equation into the first, we have:\r<BR>\n" );
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document.write( "(5 - 3y) + 3y = 4\r<BR>\n" );
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document.write( "Simplifying the equation and collecting like terms we have:<BR>\n" );
document.write( "5 - 3y + 3y = 4   or<BR>\n" );
document.write( "5 = 4\r<BR>\n" );
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document.write( "Since this clearly is a false statement, the system of equations has NO solution.\r<BR>\n" );
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document.write( "Another way to look at this problem is to get both equations into slope-intercept form y = mx + b.  We have\r<BR>\n" );
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document.write( "y = -(1/3)x + (4/3)<BR>\n" );
document.write( "y = -(1/3)x + (5/3)\r<BR>\n" );
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document.write( "In this case, the slope of each equation is -(1/3).  This means that the lines are either parallel or they are the same line.  Because the intercept is different ((4/3) in the first equation and (5/3) in the second equation)) the lines are NOT the same line, therefore they must be parallel.  Systems of equations representing parallel lines have no solution.<BR>\n" );
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